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Journal articles on the topic 'Minimal surface'

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Published: 4 June 2021

Last updated: 25 January 2023

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1

Stievenart, J. L., M. T. Iba-Zizen, A. Tourbah, A. Lopez, M. Thibierge, A. Abanou, and E. A. Cabanis. "Minimal Surface." Brain Research Bulletin 44, no. 2 (1997): 117–24. http://dx.doi.org/10.1016/s0361-9230(97)00113-5.

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2

Kungching, Chang, and James Eells. "Unstable minimal surface coboundaries." Acta Mathematica Sinica 2, no. 3 (September 1986): 233–47. http://dx.doi.org/10.1007/bf02582026.

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3

Hao, Yong-Xia, Ren-Hong Wang, and Chong-Jun Li. "Minimal quasi-Bézier surface." Applied Mathematical Modelling 36, no. 12 (December 2012): 5751–57. http://dx.doi.org/10.1016/j.apm.2012.01.040.

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4

Fang, Yi, and Jenn-Fang Hwang. "When is a minimal surface a minimal graph?" Pacific Journal of Mathematics 207, no. 2 (December 1, 2002): 359–76. http://dx.doi.org/10.2140/pjm.2002.207.359.

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5

Velimirovic, Ljubica, Grozdana Radivojevic, Mica Stankovic, and Dragan Kostic. "Minimal surfaces for architectural constructions." Facta universitatis - series: Architecture and Civil Engineering 6, no. 1 (2008): 89–96. http://dx.doi.org/10.2298/fuace0801089v.

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Minimal surfaces are the surfaces of the smallest area spanned by a given boundary. The equivalent is the definition that it is the surface of vanishing mean curvature. Minimal surface theory is rapidly developed at recent time. Many new examples are constructed and old altered. Minimal area property makes this surface suitable for application in architecture. The main reasons for application are: weight and amount of material are reduced on minimum. Famous architects like Otto Frei created this new trend in architecture. In recent years it becomes possible to enlarge the family of minimal surfaces by constructing new surfaces.

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6

Hoffman, David, and William H. Meeks. "Limits of minimal surfaces and Scherk's Fifth Surface." Archive for Rational Mechanics and Analysis 111, no. 2 (June 1990): 181–95. http://dx.doi.org/10.1007/bf00375407.

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7

Yamashita, Shinji. "Local minima of the Gauss curvature of a minimal surface." Bulletin of the Australian Mathematical Society 44, no. 3 (December 1991): 397–404. http://dx.doi.org/10.1017/s0004972700029907.

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Let D be a domain in the complex ω-plane and let x: D → R3 be a regular minimal surface. Let M(K) be the set of points ω0 ∈ D where the Gauss curvature K attains local minima: K(ω0) ≤ K(ω) for |ω – ω0| < δ(ω0), δ(ω0) < 0. The components of M(K) are of three types: isolated points; simple analytic arcs terminating nowhere in D; analytic Jordan curves in D. Components of the third type are related to the Gauss map.

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8

Morabito, Filippo. "Periodic minimal surfaces embedded in ℝ3 derived from the singly periodic Scherk minimal surface." Communications in Contemporary Mathematics 22, no. 01 (December 11, 2018): 1850075. http://dx.doi.org/10.1142/s021919971850075x.

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We construct three kinds of periodic minimal surfaces embedded in [Formula: see text] We show the existence of a [Formula: see text]-parameter family of minimal surfaces invariant under the action of a translation by [Formula: see text] which seen from a distance look like [Formula: see text] equidistant parallel planes intersecting orthogonally [Formula: see text] equidistant parallel planes, [Formula: see text] [Formula: see text] We also consider the case where the surfaces are asymptotic to [Formula: see text] equidistant parallel planes intersecting orthogonally infinitely many equidistant parallel planes. In this case, the minimal surfaces are doubly periodic, precisely they are invariant under the action of two orthogonal translations. Last we construct triply periodic minimal surfaces which are invariant under the action of three orthogonal translations in the case of two stacks of infinitely many equidistant parallel planes which intersect orthogonally.

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9

Fouladgar, K., and Leon Simon. "The symmetric minimal surface equation." Indiana University Mathematics Journal 69, no. 1 (2020): 331–66. http://dx.doi.org/10.1512/iumj.2020.69.8412.

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10

Zou, Du, and Ge Xiong. "The minimal Orlicz surface area." Advances in Applied Mathematics 61 (October 2014): 25–45. http://dx.doi.org/10.1016/j.aam.2014.08.006.

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11

Koch, E., and W. Fischer. "New surface patches for minimal balance surfaces. II. Multiple catenoids." Acta Crystallographica Section A Foundations of Crystallography 45, no. 2 (February 1, 1989): 169–74. http://dx.doi.org/10.1107/s010876738801075x.

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Eight new families of minimal balance surfaces are described. Their surface patches belong to a new kind, called multiple catenoids. The generating circuits of such a minimal surface are two congruent concave polygons with one point of self-contact each. The new minimal balance surfaces are complementary to other minimal balance surfaces which are built up from catenoid-like surface patches and have been known before.

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12

NITSCHE, J. C. C. "THE EXISTENCE OF SURFACE PATCHES FOR PERIODIC MINIMAL SURFACES." Le Journal de Physique Colloques 51, no. C7 (December 1990): C7–265—C7–271. http://dx.doi.org/10.1051/jphyscol:1990727.

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13

ARAÜJO, HENRIQUE, and MARIA LUIZA LEITE. "How many maximal surfaces do correspond to one minimal surface?" Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 1 (January 2009): 165–75. http://dx.doi.org/10.1017/s0305004108001722.

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AbstractWe discuss the minimal-to-maximal correspondence between surfaces and show that, under this correspondence, a congruence class of minimal surfaces in 3 determines an 2-family of congruence classes of maximal surfaces in 3. It is proved that further identifications among these classes may exist, depending upon the subgroup of automorphisms preserving the Hopf differential on the underlying Riemann surface. The space of maximal congruence classes inherits a quotient topology from 2. In the case of the Scherk minimal surface, the subgroup has order two and the quotient space is topologically a disc with boundary. Other classical examples are discussed: for the Enneper minimal surface, one obtains a non-Hausdorff space; for the minimal catenoid, a closed interval.

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14

Chen, Weihuan, and Yi Fang. "Self θ-congruent minimal surfaces in ℝ3." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 69, no. 2 (October 2000): 229–44. http://dx.doi.org/10.1017/s1446788700002196.

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AbstractA minimal surface is a surface with vanishing mean curvature. In this paper we study self θ -congruent minimal surfaces, that is, surfaces which are congruent to their θ-associates under rigid motions in R3 for 0 ≤ θ < 2π. We give necessary and sufficient conditions in terms of its Weierstrass pair for a surface to be self θ-congruent. We also construct some examples and give an application.

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15

Yurenkova, L. R., R. A. Maksutova, D. M. Meleshin, and M. А. Ivanov. "Minimal surfaces in science, technology, architecture." Glavnyj mekhanik (Chief Mechanic), no. 6 (June 9, 2022): 410–15. http://dx.doi.org/10.33920/pro-2-2206-09.

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The article considers minimal surfaces, the interest in which has not decreased for more than two hundred years. The minimum surface is the surface of zero mean curvature. Initially, soap bubbles and soap films tightening wire contours were examples of such surfaces. Mathematicians were the first to pay attention to these surfaces, among which are names known all over the world: Lagrange, Laplace, Poisson, Steiner, Plateau. Scientists have noticed that the analytical expression of minimal surfaces is found in research in the field of physics and chemistry, which led to discoveries awarded the Nobel Prize. Due to the unusual properties of minimal surfaces, new construction materials have appeared in the technique.

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16

Abu Muhanna, Yusuf, and Rosihan M. Ali. "Biharmonic Maps and Laguerre Minimal Surfaces." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/843156.

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A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surfaceΦis its associated surfaceΨ=1+u2Φ, whereulies in the unit disk. In this paper, the projection of the surfaceΨassociated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization ofΨis obtained under the assumption that the corresponding isotropic map of the Laguerre minimal surface is harmonic. A sufficient and necessary condition is also derived forΨto be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.

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17

Leschke, K., and K. Moriya. "The $$\mu $$-Darboux transformation of minimal surfaces." manuscripta mathematica 162, no. 3-4 (September 12, 2019): 537–58. http://dx.doi.org/10.1007/s00229-019-01142-9.

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Abstract The classical notion of the Darboux transformation of isothermic surfaces can be generalised to a transformation for conformal immersions. Since a minimal surface is Willmore, we can use the associated $$\mathbb { C}_*$$C∗-family of flat connections of the harmonic conformal Gauss map to construct such transforms, the so-called $$\mu $$μ-Darboux transforms. We show that a $$\mu $$μ-Darboux transform of a minimal surface is not minimal but a Willmore surface in 4-space. More precisely, we show that a $$\mu $$μ-Darboux transform of a minimal surface f is a twistor projection of a holomorphic curve in $$\mathbb { C}\mathbb { P}^3$$CP3 which is canonically associated to a minimal surface $$f_{p,q}$$fp,q in the right-associated family of f. Here we use an extension of the notion of the associated family $$f_{p,q}$$fp,q of a minimal surface to allow quaternionic parameters. We prove that the pointwise limit of Darboux transforms of f is the associated Willmore surface of f at $$\mu =1$$μ=1. Moreover, the family of Willmore surfaces $$\mu $$μ-Darboux transforms, $$\mu \in \mathbb { C}_*$$μ∈C∗, extends to a $$\mathbb { C}\mathbb { P}^1$$CP1 family of Willmore surfaces $$f^\mu : M \rightarrow S^4$$fμ:M→S4 where $$\mu \in \mathbb { C}\mathbb { P}^1$$μ∈CP1.

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18

HAYWARD, SEAN A. "INVOLUTE, MINIMAL, OUTER AND INCREASINGLY TRAPPED SURFACES." International Journal of Modern Physics D 20, no. 03 (March 2011): 401–11. http://dx.doi.org/10.1142/s0218271811018718.

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Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increasingly (future, respectively past) trapped surfaces generate surfaces which are more trapped in a (future, respectively past) causal variation, with three types: in any such causal variation; along the expansion vector; and in some such causal variation. This suggests a definition of doubly outer trapped surface involving two independent curvatures. This in turn suggests a definition of involute trapped surface. Adding a weaker condition, the eight conditions form an interwoven hierarchy, with four independent relations which assume the null energy condition, and another holding in a special case of symmetric curvature.

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19

Fischer, W., and E. Koch. "New surface patches for minimal balance surfaces. I. Branched catenoids." Acta Crystallographica Section A Foundations of Crystallography 45, no. 2 (February 1, 1989): 166–69. http://dx.doi.org/10.1107/s0108767388010797.

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Three new families of minimal balance surfaces have been derived. For this a new kind of surface patch,i.e.branched catenoid, has been used. A concave polygon with one point of self-contact and a convex polygon are the two generating circuits of such a minimal balance surface.

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20

FUJITA, Shinnosuke, Yoshihiro KANNO, and Makoto OHSAKI. "COMPUTATIONAL MORPHOGENESIS OF MINIMAL SURFACE REPRESENTED AS PARAMETRIC SURFACE." Journal of Structural and Construction Engineering (Transactions of AIJ) 82, no. 738 (2017): 1299–307. http://dx.doi.org/10.3130/aijs.82.1299.

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21

Ma, Tongyi. "The Minimal Dual Orlicz Surface Area." Taiwanese Journal of Mathematics 20, no. 2 (March 2016): 287–309. http://dx.doi.org/10.11650/tjm.20.2016.6632.

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22

Weber, Matthias. "On the Horgan minimal non-surface." Calculus of Variations and Partial Differential Equations 7, no. 4 (November 1, 1998): 373–79. http://dx.doi.org/10.1007/s005260050112.

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23

Kallrath, Josef, and Markus M. Frey. "Minimal Surface Convex Hulls of Spheres." Vietnam Journal of Mathematics 46, no. 4 (November 5, 2018): 883–913. http://dx.doi.org/10.1007/s10013-018-0317-8.

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24

Shibata, Keiichi. "Orthogonal stance of a minimal surface against its bounding surfaces." Tohoku Mathematical Journal 41, no. 3 (1989): 461–69. http://dx.doi.org/10.2748/tmj/1178227773.

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25

Fischer, W., and E. Koch. "New surface patches for minimal balance surfaces. III. Infinite strips." Acta Crystallographica Section A Foundations of Crystallography 45, no. 7 (July 1, 1989): 485–90. http://dx.doi.org/10.1107/s010876738900317x.

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26

Ahmad, Daud, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, and Arsha Khalid. "A Computational Model for q -Bernstein Quasi-Minimal Bézier Surface." Journal of Mathematics 2022 (September 20, 2022): 1–21. http://dx.doi.org/10.1155/2022/8994112.

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A computational model is presented to find the q -Bernstein quasi-minimal Bézier surfaces as the extremal of Dirichlet functional, and the Bézier surfaces are used quite frequently in the literature of computer science for computer graphics and the related disciplines. The recent work [1–5] on q -Bernstein–Bézier surfaces leads the way to the new generalizations of q -Bernstein polynomial Bézier surfaces for the related Plateau–Bézier problem. The q -Bernstein polynomial-based Plateau–Bézier problem is the minimal area surface amongst all the q -Bernstein polynomial-based Bézier surfaces, spanned by the prescribed boundary. Instead of usual area functional that depends on square root of its integrand, we choose the Dirichlet functional. Related Euler–Lagrange equation is a partial differential equation, for which solutions are known for a few special cases to obtain the corresponding minimal surface. Instead of solving the partial differential equation, we can find the optimal conditions for which the surface is the extremal of the Dirichlet functional. We workout the minimal Bézier surface based on the q -Bernstein polynomials as the extremal of Dirichlet functional by determining the vanishing condition for the gradient of the Dirichlet functional for prescribed boundary. The vanishing condition is reduced to a system of algebraic constraints, which can then be solved for unknown control points in terms of known boundary control points. The resulting Bézier surface is q -Bernstein–Bézier minimal surface.

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27

Mladenov, Ivaïlo M., and Mariana Ts Hadzhilazova. "Geometry of the anisotropic minimal surfaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 2 (June 1, 2012): 79–88. http://dx.doi.org/10.2478/v10309-012-0042-3.

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Abstract A simple modification of the surface tension in the axisymmetric case leads to analogues of the Delaunay surfaces. Here we have derived an explicit parameterization of the most simple case of this new class of surfaces which can be considered as a generalization of the catenoids. The geometry of these surfaces depends on two real parameters and has been studied in some detail

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28

Griffin, Sarah Field. "Minimal Surfaces: A Derivation of the Minimal Surface Equation for an Arbitrary ${\mathbb{C}}^2$ Coordinate Chart." Missouri Journal of Mathematical Sciences 13, no. 3 (October 2001): 145–53. http://dx.doi.org/10.35834/2001/1303145.

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29

Lee, Hojoo. "Minimal surface systems, maximal surface systems and special Lagrangian equations." Transactions of the American Mathematical Society 365, no. 7 (November 7, 2012): 3775–97. http://dx.doi.org/10.1090/s0002-9947-2012-05786-2.

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30

Eriksson, Jan Christer, and Stig Ljunggren. "The Mechanical Surface Tension and Stability of Minimal Surface Structures." Journal of Colloid and Interface Science 167, no. 2 (October 1994): 227–31. http://dx.doi.org/10.1006/jcis.1994.1356.

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31

Koch, E., and W. Fischer. "Flat points of minimal balance surfaces." Acta Crystallographica Section A Foundations of Crystallography 46, no. 1 (January 1, 1990): 33–40. http://dx.doi.org/10.1107/s010876738900927x.

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The symmetry conditions for flat points of minimal surfaces have been studied in relation to the order β of points on such surfaces. Using symmetry aspects, a set of rules for the derivation of fiat points have been developed. By means of these rules the flat points for the 45 families of minimal balance surfaces known so far have been determined. As a check for completeness the relation between the genus of a minimal surface and the orders of its flat points has been used.

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32

da Silva, Márcio Fabiano, Guillermo Antonio Lobos, and Valério Ramos Batista. "Minimal Surfaces with Only Horizontal Symmetries." ISRN Geometry 2011 (July 19, 2011): 1–19. http://dx.doi.org/10.5402/2011/943462.

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The Schwarz reflection principle states that a minimal surface S in ℝ3 is invariant under reflections in the plane of its principal geodesics and also invariant under 180°-rotations about its straight lines. We find new examples of embedded triply periodic minimal surfaces for which such symmetries are all of horizontal type.

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33

Anciaux, Henri, Brendan Guilfoyle, and Pascal Romon. "Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface." Journal of Geometry and Physics 61, no. 1 (January 2011): 237–47. http://dx.doi.org/10.1016/j.geomphys.2010.09.017.

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34

KIM, YOUNG WOOK, SUNG-EUN KOH, HEAYONG SHIN, and SEONG-DEOG YANG. "HELICOIDAL MINIMAL SURFACES IN ℍ2×ℝ." Bulletin of the Australian Mathematical Society 86, no. 1 (December 15, 2011): 135–49. http://dx.doi.org/10.1017/s0004972711003042.

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AbstractIt is shown that a minimal surface in ℍ2×ℝ is invariant under a one-parameter group of screw motions if and only if it lies in the associate family of helicoids. It is also shown that the conjugate surfaces of the parabolic and hyperbolic helicoids in ℍ2×ℝ are certain types of catenoids.

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35

Ejiri, Norio, and Toshihiro Shoda. "The Existence of rG Family and tG Family, and Their Geometric Invariants." Mathematics 8, no. 10 (October 2, 2020): 1693. http://dx.doi.org/10.3390/math8101693.

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In the 1990s, physicists constructed two one-parameter families of compact oriented embedded minimal surfaces in flat three-tori by using symmetries of space groups, called the rG family and tG family. The present work studies the existence of the two families via the period lattices. Moreover, we will consider two kinds of geometric invariants for the two families, namely, the Morse index and the signature of a minimal surface. We show that Schwarz P surface, D surface, Schoen’s gyroid, and the Lidinoid belong to a family of minimal surfaces with Morse index 1.

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36

BUKHTYAK, Mikhail Stepanovych. "A COMPOSITE SURFACE CLOSE TO PSEUDO-MINIMAL." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 46 (April 1, 2017): 5–13. http://dx.doi.org/10.17223/19988621/46/1.

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37

Haigh, Gordon. "69.17 Cross-Sections and Minimal Surface Area." Mathematical Gazette 69, no. 448 (June 1985): 122. http://dx.doi.org/10.2307/3616933.

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38

Chodosh, Otis, and Davi Maximo. "The Morse Index of a Minimal Surface." Notices of the American Mathematical Society 68, no. 06 (June 1, 2021): 1. http://dx.doi.org/10.1090/noti2291.

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39

Meeks, W. H. "Geometric results in classical minimal surface theory." Surveys in Differential Geometry 8, no. 1 (2003): 269–306. http://dx.doi.org/10.4310/sdg.2003.v8.n1.a10.

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40

Meeks, W. H., and J. Pérez. "Conformal properties in classical minimal surface theory." Surveys in Differential Geometry 9, no. 1 (2004): 275–335. http://dx.doi.org/10.4310/sdg.2004.v9.n1.a8.

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41

Neumann, Walter D., Helge Møller Pedersen, and Anne Pichon. "Minimal surface singularities are Lipschitz normally embedded." Journal of the London Mathematical Society 101, no. 2 (September 12, 2019): 641–58. http://dx.doi.org/10.1112/jlms.12280.

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42

Christensen, J., Z. Liang, and M. Willatzen. "Minimal model for spoof acoustoelastic surface states." AIP Advances 4, no. 12 (December 2014): 124301. http://dx.doi.org/10.1063/1.4901282.

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43

Aliev, A. N., J. Kalaycı, and Y. Nutku. "General minimal surface solution for gravitational instantons." Physical Review D 56, no. 2 (July 15, 1997): 1332–33. http://dx.doi.org/10.1103/physrevd.56.1332.

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44

Kuwert, Ernst Christoph. "Embedded solutions for exterior minimal surface problems." Manuscripta Mathematica 70, no. 1 (December 1991): 51–65. http://dx.doi.org/10.1007/bf02568361.

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45

Simon, Leon. "Entire solutions of the minimal surface equation." Journal of Differential Geometry 30, no. 3 (1989): 643–88. http://dx.doi.org/10.4310/jdg/1214443827.

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46

Osting, Braxton, and Dominique Zosso. "A minimal surface criterion for graph partitioning." Inverse Problems and Imaging 10, no. 4 (October 2016): 1149–80. http://dx.doi.org/10.3934/ipi.2016036.

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47

Bors, A. G., and Ming Luo. "Optimized 3D Watermarking for Minimal Surface Distortion." IEEE Transactions on Image Processing 22, no. 5 (May 2013): 1822–35. http://dx.doi.org/10.1109/tip.2012.2236345.

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48

Traizet, Martin. "An Embedded Minimal Surface with no Symmetries." Journal of Differential Geometry 60, no. 1 (January 2002): 103–53. http://dx.doi.org/10.4310/jdg/1090351085.

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49

Kolatan, Sulan. "Minimal Surface Geometry and the Green Paradigm." Architectural Design 78, no. 6 (November 2008): 62–67. http://dx.doi.org/10.1002/ad.771.

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50

Gao, David Yang, and Wei H. Yang. "Multi-Duality in Minimal Surface-Type Problems." Studies in Applied Mathematics 95, no. 2 (August 1995): 127–46. http://dx.doi.org/10.1002/sapm1995952127.

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