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Journal articles on the topic 'Diffusions on manifolds with singularities'

Author: Grafiati

Published: 14 March 2023

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1

Antonelli, P. L., and T. J. Zastawniak. "Diffusions on Finsler manifolds." Reports on Mathematical Physics 33, no. 1-2 (August 1993): 303–15. http://dx.doi.org/10.1016/0034-4877(93)90065-m.

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2

Natanzon, S. M. "Singularities and noncommutative Frobenius manifolds." Proceedings of the Steklov Institute of Mathematics 259, no. 1 (December 2007): 137–48. http://dx.doi.org/10.1134/s0081543807040104.

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3

Liu, Zhong-Dong, Zhongmin Shen, and Dagang Yang. "Riemannian Manifolds with Conical Singularities." Rocky Mountain Journal of Mathematics 28, no. 2 (June 1998): 625–41. http://dx.doi.org/10.1216/rmjm/1181071789.

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4

Schrohe, Elmar. "Complex powers on noncompact manifolds and manifolds with singularities." Mathematische Annalen 281, no. 3 (August 1988): 393–409. http://dx.doi.org/10.1007/bf01457152.

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5

Chiu, Hung-Lin. "SINGULARITIES AND SOME INVARIANTS OF SINGULARITIES IN CONTACT 3-MANIFOLDS." Taiwanese Journal of Mathematics 10, no. 5 (September 2006): 1391–408. http://dx.doi.org/10.11650/twjm/1500557309.

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6

Lyons, Russell. "Diffusions and Random Shadows in Negatively Curved Manifolds." Journal of Functional Analysis 138, no. 2 (June 1996): 426–48. http://dx.doi.org/10.1006/jfan.1996.0071.

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7

Smith, P. D., and Deane Yang. "Removing point singularities of Riemannian manifolds." Transactions of the American Mathematical Society 333, no. 1 (January 1, 1992): 203–19. http://dx.doi.org/10.1090/s0002-9947-1992-1052910-2.

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8

Ma, L., and B. W. Schulze. "Operators on manifolds with conical singularities." Journal of Pseudo-Differential Operators and Applications 1, no. 1 (March 10, 2010): 55–74. http://dx.doi.org/10.1007/s11868-010-0002-5.

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9

Plamenevskii, B. A., and V. N. Senichkin. "Pseudodifferential operators on manifolds with singularities." Functional Analysis and Its Applications 33, no. 2 (April 1999): 154–56. http://dx.doi.org/10.1007/bf02465199.

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10

Stoica, Ovidiu Cristinel. "The geometry of warped product singularities." International Journal of Geometric Methods in Modern Physics 14, no. 02 (January 18, 2017): 1750024. http://dx.doi.org/10.1142/s0219887817500244.

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In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

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11

Malyshev, Dmitry. "Del Pezzo Singularities and SUSY Breaking." Advances in High Energy Physics 2011 (2011): 1–30. http://dx.doi.org/10.1155/2011/630892.

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An analytic construction of compact Calabi-Yau manifolds with del Pezzo singularities is found. We present complete intersection CY manifolds for all del Pezzo singularities and study the complex deformations of these singularities. An example of the quintic CY manifold with del Pezzo 6 singularity and some number of conifold singularities is studied in detail. The possibilities for the ‘‘geometric’’ and ISS mechanisms of dynamical SUSY breaking are discussed. As an example, we construct the ISS vacuum for the del Pezzo 6 singularity.

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12

Davis, M. H. A., and M. P. Spathopoulos. "On the Minimum Principle for Controlled Diffusions on Manifolds." SIAM Journal on Control and Optimization 27, no. 5 (September 1989): 1092–107. http://dx.doi.org/10.1137/0327058.

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13

Savin, A. Yu, and B. Yu Sternin. "Elliptic translators on manifolds with point singularities." Differential Equations 48, no. 12 (December 2012): 1577–85. http://dx.doi.org/10.1134/s001226611212004x.

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14

Savin, A. Yu, and B. Yu Sternin. "Elliptic translators on manifolds with multidimensional singularities." Differential Equations 49, no. 4 (April 2013): 494–509. http://dx.doi.org/10.1134/s0012266113040101.

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15

Vassiliev, D. G. "Pseudo-Differential Operators on Manifolds with Singularities." Bulletin of the London Mathematical Society 25, no. 2 (March 1993): 203–4. http://dx.doi.org/10.1112/blms/25.2.203b.

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16

Bilal, Adel, and Steffen Metzger. "Compact weak G2-manifolds with conical singularities." Nuclear Physics B 663, no. 1-2 (July 2003): 343–64. http://dx.doi.org/10.1016/s0550-3213(03)00388-2.

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17

Rosinger, Elemér E. "Differential Algebras with Dense Singularities on Manifolds." Acta Applicandae Mathematicae 95, no. 3 (March 31, 2007): 233–56. http://dx.doi.org/10.1007/s10440-007-9088-z.

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18

Hein, Hans-Joachim, and Song Sun. "Calabi-Yau manifolds with isolated conical singularities." Publications mathématiques de l'IHÉS 126, no. 1 (August 25, 2017): 73–130. http://dx.doi.org/10.1007/s10240-017-0092-1.

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19

Takahashi, Atsushi, and Yuuki Shiraishi. "On the Frobenius manifolds for cusp singularities." Advances in Mathematics 273 (March 2015): 485–522. http://dx.doi.org/10.1016/j.aim.2014.12.019.

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20

Falbel, Elisha. "Non-embeddable CR-manifolds and surface singularities." Inventiones Mathematicae 108, no. 1 (December 1992): 49–65. http://dx.doi.org/10.1007/bf02100599.

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21

Schrohe, Elmar. "Noncommutative Residues and Manifolds with Conical Singularities." Journal of Functional Analysis 150, no. 1 (October 1997): 146–74. http://dx.doi.org/10.1006/jfan.1997.3109.

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22

Sadykov, Rustam. "Elimination of singularities of smooth mappings of 4-manifolds into 3-manifolds." Topology and its Applications 144, no. 1-3 (October 2004): 173–99. http://dx.doi.org/10.1016/j.topol.2004.04.006.

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23

Izumiya, Shyuichi, Kentaro Saji, and Nobuko Takeuchi. "Singularities of line congruences." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 6 (December 2003): 1341–59. http://dx.doi.org/10.1017/s0308210500002973.

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A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.

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24

SPRING, DAVID. "DIRECTED EMBEDDINGS OF CLOSED MANIFOLDS." Communications in Contemporary Mathematics 07, no. 05 (October 2005): 707–25. http://dx.doi.org/10.1142/s0219199705001891.

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Gromov's theorem on directed embeddings of open manifolds is generalized to the case of closed manifolds, where the embeddings are directed with respect to a given codimension ≥ 1 foliation on the manifold. Applications include directed embeddings with prescribed codimension 1 cusp singularities.

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25

Davis, M. H. A. "The Wiener space derivative for functionals of diffusions on manifolds." Nonlinearity 1, no. 1 (February 1, 1988): 241–51. http://dx.doi.org/10.1088/0951-7715/1/1/010.

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26

Sturm, Karl-Theodor. "Convex functionals of probability measures and nonlinear diffusions on manifolds." Journal de Mathématiques Pures et Appliquées 84, no. 2 (February 2005): 149–68. http://dx.doi.org/10.1016/j.matpur.2004.11.002.

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27

Gong, Guanglu, and Minping Qian. "Entropy production of stationary diffusions on non-compact Riemannian manifolds." Science in China Series A: Mathematics 40, no. 9 (September 1997): 926–31. http://dx.doi.org/10.1007/bf02878672.

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28

Arnaudon, Marc, and Ana Bela Cruzeiro. "Lagrangian Navier–Stokes diffusions on manifolds: Variational principle and stability." Bulletin des Sciences Mathématiques 136, no. 8 (December 2012): 857–81. http://dx.doi.org/10.1016/j.bulsci.2012.06.007.

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29

Elworthy, K. D., and Zhi-Ming Ma. "Admissible vector fields and related diffusions on infinite-dimensional manifolds." Ukrainian Mathematical Journal 49, no. 3 (March 1997): 451–66. http://dx.doi.org/10.1007/bf02487242.

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30

Karigiannis, Spiro. "Desingularization of G2 manifolds with isolated conical singularities." Geometry & Topology 13, no. 3 (March 3, 2009): 1583–655. http://dx.doi.org/10.2140/gt.2009.13.1583.

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31

Deeley, Robin. "Index theory for manifolds with Baas–Sullivan singularities." Journal of Noncommutative Geometry 12, no. 1 (March 23, 2018): 1–28. http://dx.doi.org/10.4171/jncg/269.

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32

Janeczko, Stanislaw, and Adam Kowalczyk. "Equivariant Singularities of Lagrangian Manifolds and Uniaxial Ferromagnet." SIAM Journal on Applied Mathematics 47, no. 6 (December 1987): 1342–60. http://dx.doi.org/10.1137/0147088.

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33

Krupa, M., and P. Szmolyan. "Extending slow manifolds near transcritical and pitchfork singularities." Nonlinearity 14, no. 6 (September 18, 2001): 1473–91. http://dx.doi.org/10.1088/0951-7715/14/6/304.

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34

Simányi, Nándor. "Singularities and non-hyperbolic manifolds do not coincide." Nonlinearity 26, no. 6 (May 9, 2013): 1703–17. http://dx.doi.org/10.1088/0951-7715/26/6/1703.

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35

Mooers, Edith A. "Heat kernel asymptotics on manifolds with conic singularities." Journal d'Analyse Mathématique 78, no. 1 (December 1999): 1–36. http://dx.doi.org/10.1007/bf02791127.

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36

Dai, Xianzhe, and Changliang Wang. "Perelman’s $$\lambda $$-Functional on Manifolds with Conical Singularities." Journal of Geometric Analysis 28, no. 4 (December 13, 2017): 3657–89. http://dx.doi.org/10.1007/s12220-017-9971-4.

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37

Vasil’ev, V. B. "Pseudodifferential Equations on Manifolds with Complicated Boundary Singularities." Journal of Mathematical Sciences 230, no. 1 (February 26, 2018): 175–83. http://dx.doi.org/10.1007/s10958-018-3737-9.

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38

Savin, A. Yu, and B. Yu Sternin. "Elliptic G-Operators on Manifolds with Isolated Singularities." Journal of Mathematical Sciences 233, no. 6 (August 4, 2018): 930–48. http://dx.doi.org/10.1007/s10958-018-3973-z.

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39

Acharya, Bobby S., and Sergei Gukov. "M theory and singularities of exceptional holonomy manifolds." Physics Reports 392, no. 3 (March 2004): 121–89. http://dx.doi.org/10.1016/j.physrep.2003.10.017.

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40

Du, Rong, Hing Sun Luk, and Stephen Yau. "New invariants for complex manifolds and isolated singularities." Communications in Analysis and Geometry 19, no. 5 (2011): 991–1021. http://dx.doi.org/10.4310/cag.2011.v19.n5.a7.

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41

Du, Rong, and Yun Gao. "New invariants for complex manifolds and rational singularities." Pacific Journal of Mathematics 269, no. 1 (July 15, 2014): 73–97. http://dx.doi.org/10.2140/pjm.2014.269.73.

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42

Weinstein, Gilbert. "Harmonic Maps with Prescribed Singularities into Hadamard Manifolds." Mathematical Research Letters 3, no. 6 (1996): 835–44. http://dx.doi.org/10.4310/mrl.1996.v3.n6.a11.

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43

Dai, Xianzhe, and Changliang Wang. "Perelman’s $W$-functional on manifolds with conical singularities." Mathematical Research Letters 27, no. 3 (2020): 665–85. http://dx.doi.org/10.4310/mrl.2020.v27.n3.a3.

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44

Tosatti, Valentino. "Families of Calabi–Yau Manifolds and Canonical Singularities." International Mathematics Research Notices 2015, no. 20 (2015): 10586–94. http://dx.doi.org/10.1093/imrn/rnv001.

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45

Zot’ev, D. B. "Kostant Prequantization of Symplectic Manifolds with Contact Singularities." Mathematical Notes 105, no. 5-6 (May 2019): 846–63. http://dx.doi.org/10.1134/s0001434619050225.

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46

Boscain, Ugo, Ludovic Sacchelli, and Mario Sigalotti. "Generic singularities of line fields on 2D manifolds." Differential Geometry and its Applications 49 (December 2016): 326–50. http://dx.doi.org/10.1016/j.difgeo.2016.09.003.

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47

Hasegawa, Masaru, Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara, and Kotaro Yamada. "Intrinsic properties of surfaces with singularities." International Journal of Mathematics 26, no. 04 (April 2015): 1540008. http://dx.doi.org/10.1142/s0129167x1540008x.

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In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in R3 are Kossowski metrics, and the pull-back metrics of surfaces consisting only of cross cap singularities are Whitney metrics. Since the singular sets of Kossowski metrics are the union of regular curves on the domains of definitions, and Whitney metrics admit only isolated singularities, these two classes of metrics are disjoint. In this paper, we give several characterizations of intrinsic invariants of cuspidal edges and cross caps in these classes of metrics. Moreover, we prove Gauss–Bonnet type formulas for Kossowski metrics and for Whitney metrics on compact 2-manifolds.

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48

BELHAJ, A., and E. H. SAIDI. "ON HYPER-KAHLER SINGULARITIES." Modern Physics Letters A 15, no. 29 (September 21, 2000): 1767–79. http://dx.doi.org/10.1142/s0217732300001638.

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Using a geometric realization of the SU (2)R symmetry and a procedure of factorization of the gauge and SU (2)R charges, we study the small instanton singularities of the Higgs branch of supersymmetric U (1)r gauge theories with eight supercharges. We derive new solutions for the moduli space of vacua preserving manifestly the eight supercharges. In particular, we obtain an extension of the ordinary ADE singularities for hyper-Kahler manifolds and show that the classical moduli space of vacua is in general given by cotangent bundles of compact weighted projective spaces.

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49

Huguet, Baptiste. "Intertwining relations for diffusions in manifolds and applications to functional inequalities." Stochastic Processes and their Applications 145 (March 2022): 1–28. http://dx.doi.org/10.1016/j.spa.2021.11.004.

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50

Shamarova, Evelina. "Chernoff's theorem for backward propagators and applications to diffusions on manifolds." Operators and Matrices, no. 4 (2011): 619–32. http://dx.doi.org/10.7153/oam-05-45.

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