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Статті в журналах з теми "Manifolds with ends"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

BELEGRADEK, IGOR. "AN ASSORTMENT OF NEGATIVELY CURVED ENDS." Journal of Topology and Analysis 05, no. 04 (December 2013): 439–49. http://dx.doi.org/10.1142/s1793525313500180.

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Анотація:

Motivated by recent groundbreaking work of Ontaneda, we describe a sizable class of closed manifolds such that the product of each manifold in the class with ℝ admits a complete metric of bounded negative sectional curvature which is an exponentially warped near one end and has finite volume near the other end.

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2

Apanasov, Boris, and Xiangdong Xie. "Geometrically Finite Complex Hyperbolic Manifolds." International Journal of Mathematics 08, no. 06 (September 1997): 703–57. http://dx.doi.org/10.1142/s0129167x97000378.

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The aim of this paper is to study geometry and topology of geometrically finite complex hyperbolic manifolds, especially their ends, as well as geometry of their holonomy groups. This study is based on our structural theorem for discrete groups acting on Heisenberg groups, on the fiber bundle structure of Heisenberg manifolds, and on the existence of finite coverings of a geometrically finite manifold such that their parabolic ends have either Abelian or 2-step nilpotent holonomy. We also study an interplay between Kähler geometry of complex hyperbolic n-manifolds and Cauchy–Riemannian geometry of their boundary (2n-1)-manifolds at infinity, and this study is based on homotopy equivalence of manifolds and isomorphism of fundamental groups.

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3

Gilligan, B., K. Oeljeklaus, and W. Richthofer. "Homogeneous Complex Manifolds with more than One End." Canadian Journal of Mathematics 41, no. 1 (February 1, 1989): 163–77. http://dx.doi.org/10.4153/cjm-1989-008-4.

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For homogeneous spaces of a (real) Lie group one of the fundamental results concerning ends (in the sense of Freudenthal [8] ) is due to A. Borel [6]. He showed that if X = G/H is the homogeneous space of a connected Lie group G by a closed connected subgroup H, then X has at most two ends. And if X does have two ends, then it is diffeomorphic to the product of R with the orbit of a maximal compact subgroup of G.In the setting of homogeneous complex manifolds the basic idea should be to find conditions which imply that the space has at most two ends and then, when the space has exactly two ends, to display the ends via bundles involving C* and compact homogeneous complex manifolds. An analytic condition which ensures that a homogeneous complex manifold X has at most two ends is that X have non-constant holomorphic functions and the structure of such a space with exactly two ends is determined, namely, it fibers over an affine homogeneous cone with its vertex removed with the fiber being compact [9], [13].

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4

Canary, Richard D. "Ends of Hyperbolic 3-Manifolds." Journal of the American Mathematical Society 6, no. 1 (January 1993): 1. http://dx.doi.org/10.2307/2152793.

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5

Canary, Richard D. "Ends of hyperbolic $3$-manifolds." Journal of the American Mathematical Society 6, no. 1 (January 1, 1993): 1. http://dx.doi.org/10.1090/s0894-0347-1993-1166330-8.

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6

Eschenburg, J. H., and V. Schroeder. "Riemannian manifolds with flat ends." Mathematische Zeitschrift 196, no. 4 (December 1987): 573–89. http://dx.doi.org/10.1007/bf01160897.

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7

Biringer, Ian, and Jean Raimbault. "Ends of unimodular random manifolds." Proceedings of the American Mathematical Society 145, no. 9 (March 23, 2017): 4021–29. http://dx.doi.org/10.1090/proc/13531.

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8

Apanasov, B. N. "Cusp ends of hyperbolic manifolds." Annals of Global Analysis and Geometry 3, no. 1 (1985): 1–11. http://dx.doi.org/10.1007/bf00054488.

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9

Alpern, S., and V. Prasad. "End Behaviour and Ergodicity for Homeomorphisms of Manifolds with Finitely Many Ends." Canadian Journal of Mathematics 39, no. 2 (April 1, 1987): 473–91. http://dx.doi.org/10.4153/cjm-1987-020-5.

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Анотація:

The recent paper of Berlanga and Epstein [5] demonstrated the significant role played by the “ends” of a noncompact manifold M in answering questions relating homeomorphisms of M to measures on M. In this paper we show that an analysis of the end behaviour of measure preserving homeomorphisms of a manifold also leads to an understanding of some of their ergodic properties, and allows results previously obtained for compact manifolds to be extended (with qualifications) to the noncompact case. We will show that ergodicity is typical (dense Gδ) with respect to various compact-open topology closed subsets of the space consisting of all homeomorphisms of a manifold M which preserve a measure μ. It may be interesting for topologists to note that we prove when M is a σ-compact connected n-manifold, n≧ 2, then M is the countable union of an increasing family of compact connected manifolds. If M is a PL or smooth manifold, this is well known and easy. If M is just, however, a topological n-manifold then we apply the recent results [9] and [12] to prove the result. The Borel measure μ, is taken to be nonatomic, locally finite, positive on open sets, and zero for the manifold boundary of M.

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10

Fujiwara, Koji, and Takashi Shioya. "Graph manifolds as ends of negatively curved Riemannian manifolds." Geometry & Topology 24, no. 4 (November 10, 2020): 2035–74. http://dx.doi.org/10.2140/gt.2020.24.2035.

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11

Ballmann, Werner, Jochen Brüning, and Gilles Carron. "Index theorems on manifolds with straight ends." Compositio Mathematica 148, no. 6 (October 15, 2012): 1897–968. http://dx.doi.org/10.1112/s0010437x12000401.

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AbstractWe study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume.

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12

Siddiqui, Aliya, Young Suh та Oğuzhan Bahadır. "Extremities for statistical submanifolds in Кenmotsu statistical manifolds". Filomat 35, № 2 (2021): 591–603. http://dx.doi.org/10.2298/fil2102591s.

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Анотація:

Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properties of Kenmotsu statistical manifolds. It has been shown that a Kenmotsu statistical manifold is not a Ricci-flat statistical manifold by constructing a counter-example. Finally, we prove a very well-known Chen-Ricci inequality for statistical submanifolds in Kenmotsu statistical manifolds of constant ?-sectional curvature by adopting optimization techniques on submanifolds. This article ends with some concluding remarks.

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13

Ilyutko, Denis P., and Evgeny A. Sevost’yanov. "On prime ends on Riemannian manifolds." Journal of Mathematical Sciences 241, no. 1 (July 12, 2019): 47–63. http://dx.doi.org/10.1007/s10958-019-04406-7.

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14

Grigor’yan, Alexander, and Laurent Saloff-Coste. "Heat kernel on manifolds with ends." Annales de l’institut Fourier 59, no. 5 (2009): 1917–97. http://dx.doi.org/10.5802/aif.2480.

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15

Coriasco, Sandro, and Lidia Maniccia. "On the Spectral Asymptotics of Operators on Manifolds with Ends." Abstract and Applied Analysis 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/909782.

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We deal with the asymptotic behaviour, forλ→+∞, of the counting functionNP(λ)of certain positive self-adjoint operatorsPwith double order(m,μ),m,μ>0, m≠μ, defined on a manifold with endsM. The structure of this class of noncompact manifolds allows to make use of calculi of pseudodifferential operators and Fourier integral operators associated with weighted symbols globally defined onℝn. By means of these tools, we improve known results concerning the remainder terms of the Weyl Formulae forNP(λ)and show how their behaviour depends on the ratiom/μand the dimension ofM.

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16

Vaisman, Izu. "Locally conformal symplectic manifolds." International Journal of Mathematics and Mathematical Sciences 8, no. 3 (1985): 521–36. http://dx.doi.org/10.1155/s0161171285000564.

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A locally conformal symplectic (l. c. s.) manifold is a pair(M2n,Ω)whereM2n(n>1)is a connected differentiable manifold, andΩa nondegenerate2-form onMsuch thatM=⋃αUα(Uα- open subsets).Ω/Uα=eσαΩα,σα:Uα→ℝ,dΩα=0. Equivalently,dΩ=ω∧Ωfor some closed1-formω. L. c. s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetic canonical transformations. The paper discusses first Hamiltonian vector fields, and infinitesimal automorphisms (i. a.) on l. c. s. manifolds. If(M,Ω)has an i. a.Xsuch thatω(X)≠0, we say thatMis of the first kind andΩassumes the particular formΩ=dθ−ω∧θ. Such anMis a2-contact manifold with the structure forms(ω,θ), and it has a vertical2-dimensional foliationV. IfVis regular, we can give a fibration theorem which shows thatMis aT2-principal bundle over a symplectic manifold. Particularly,Vis regular for some homogeneous l. c. s, manifolds, and this leads to a general construction of compact homogeneous l. c. s, manifolds. Various related geometric results, including reductivity theorems for Lie algebras of i. a. are also given. Most of the proofs are adaptations of corresponding proofs in symplectic and contact geometry. The paper ends with an Appendix which states an analogous fibration theorem in Riemannian geometry.

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17

Shen, Zhongmin. "On complete Riemannian manifolds with collapsed ends." Pacific Journal of Mathematics 163, no. 1 (March 1, 1994): 175–82. http://dx.doi.org/10.2140/pjm.1994.163.175.

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18

Bouclet, Jean-Marc. "Littlewood-Paley decompositions on manifolds with ends." Bulletin de la Société mathématique de France 138, no. 1 (2010): 1–37. http://dx.doi.org/10.24033/bsmf.2584.

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19

Parnovski, L. "Scattering Matrix for Manifolds with Conical Ends." Journal of the London Mathematical Society 61, no. 2 (April 2000): 555–67. http://dx.doi.org/10.1112/s0024610799008534.

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20

Curry, Sean, Álvaro Pelayo, and Xiudi Tang. "Symplectic Stability on Manifolds with Cylindrical Ends." Journal of Geometric Analysis 29, no. 2 (July 10, 2018): 1660–75. http://dx.doi.org/10.1007/s12220-018-0057-8.

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21

Ito, K., and E. Skibsted. "Radiation condition bounds on manifolds with ends." Journal of Functional Analysis 278, no. 9 (May 2020): 108449. http://dx.doi.org/10.1016/j.jfa.2019.108449.

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22

Korol’kov, S. A. "Harmonic functions on Riemannian manifolds with ends." Siberian Mathematical Journal 49, no. 6 (November 2008): 1051–61. http://dx.doi.org/10.1007/s11202-008-0101-1.

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23

Carron, C. "L2 -cohomology of manifolds with flat ends." Geometric and Functional Analysis 13, no. 2 (February 2003): 366–95. http://dx.doi.org/10.1007/s000390300009.

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24

Christiansen, Tanya, and Maciej Zworski. "Spectral asymptotics for manifolds with cylindrical ends." Annales de l’institut Fourier 45, no. 1 (1995): 251–63. http://dx.doi.org/10.5802/aif.1455.

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25

Bouclet, Jean-Marc, and Yannick Sire. "Refined Sobolev inequalities on manifolds with ends." Mathematical Research Letters 21, no. 4 (2014): 633–75. http://dx.doi.org/10.4310/mrl.2014.v21.n4.a3.

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26

Bui, The Anh. "Littlewood-Paley Inequalities on Manifolds with Ends." Potential Analysis 53, no. 2 (May 1, 2019): 613–29. http://dx.doi.org/10.1007/s11118-019-09780-0.

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27

Avramidi, Grigori. "Ends of finite volume, nonpositively curved manifolds." Mathematische Annalen 373, no. 1-2 (June 12, 2018): 191–235. http://dx.doi.org/10.1007/s00208-018-1698-4.

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28

Charitos, Charalambos. "Compressible ends of leaves in foliated 3-manifolds." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 63, no. 2 (October 1997): 208–17. http://dx.doi.org/10.1017/s1446788700000641.

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29

Cai, Mingliang, Tobias Holck Colding, and DaGang Yang. "A gap theorem for ends of complete manifolds." Proceedings of the American Mathematical Society 123, no. 1 (January 1, 1995): 247. http://dx.doi.org/10.1090/s0002-9939-1995-1213856-8.

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30

Guilbault, Craig R. "Noncollarable ends of $4$-manifolds: some realization theorems." Michigan Mathematical Journal 41, no. 1 (1994): 87–95. http://dx.doi.org/10.1307/mmj/1029004916.

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31

Bižaca, Žarko, and John Etnyre. "Smooth structures on collarable ends of 4-manifolds." Topology 37, no. 3 (May 1998): 461–67. http://dx.doi.org/10.1016/s0040-9383(97)00046-3.

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32

Hempel, Rainer, Olaf Post, and Ricardo Weder. "On open scattering channels for manifolds with ends." Journal of Functional Analysis 266, no. 9 (May 2014): 5526–83. http://dx.doi.org/10.1016/j.jfa.2014.01.025.

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33

Minsky, Yair N. "Teichmüller geodesics and ends of hyperbolic 3-manifolds." Topology 32, no. 3 (July 1993): 625–47. http://dx.doi.org/10.1016/0040-9383(93)90013-l.

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34

Garity, Dennis, and Dušan Repovš. "Homogeneity groups of ends of open 3-manifolds." Pacific Journal of Mathematics 269, no. 1 (July 15, 2014): 99–112. http://dx.doi.org/10.2140/pjm.2014.269.99.

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35

Christiansen, T. "Scattering Theory for Manifolds with Asymptotically Cylindrical Ends." Journal of Functional Analysis 131, no. 2 (August 1995): 499–530. http://dx.doi.org/10.1006/jfan.1995.1097.

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36

Korolkov, S. A., and A. G. Losev. "Generalized harmonic functions of Riemannian manifolds with ends." Mathematische Zeitschrift 272, no. 1-2 (October 8, 2011): 459–72. http://dx.doi.org/10.1007/s00209-011-0943-2.

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37

Krainer, Thomas. "Elliptic boundary problems on manifolds with polycylindrical ends." Journal of Functional Analysis 244, no. 2 (March 2007): 351–86. http://dx.doi.org/10.1016/j.jfa.2006.09.018.

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38

ZHU, PENG. "L 2 harmonic forms and finiteness of ends." Anais da Academia Brasileira de Ciências 85, no. 2 (June 2013): 457–71. http://dx.doi.org/10.1590/s0001-37652013000200003.

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39

Kakimizu, Osamu. "Finding boundary for the semistable ends of 3-manifolds." Hiroshima Mathematical Journal 17, no. 2 (1987): 395–403. http://dx.doi.org/10.32917/hmj/1206130076.

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40

Fernández-Bretón, David, and Nicholas G. Vlamis. "Ends of non-metrizable manifolds: A generalized bagpipe theorem." Topology and its Applications 310 (April 2022): 108017. http://dx.doi.org/10.1016/j.topol.2022.108017.

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41

xiaoyun, Ma, and Robert C. McOwen. "The kaplacian on complete manifolds with warped cylindrical ends." Communications in Partial Differential Equations 16, no. 10 (January 1991): 1583–614. http://dx.doi.org/10.1080/03605309108820814.

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42

Lauter, Robert, and Sergiu Moroianu. "An index formula on manifolds with fibered cusp ends." Journal of Geometric Analysis 15, no. 2 (June 2005): 261–83. http://dx.doi.org/10.1007/bf02922196.

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43

Lee, Yi-Jen. "Seiberg-Witten Equations on Three-manifolds with Euclidean Ends." Communications in Analysis and Geometry 13, no. 1 (2005): 1–88. http://dx.doi.org/10.4310/cag.2005.v13.n1.a1.

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44

Anderson, James W., Kurt Falk, and Pekka Tukia. "CONFORMAL MEASURES ASSOCIATED TO ENDS OF HYPERBOLIC n-MANIFOLDS." Quarterly Journal of Mathematics 58, no. 1 (November 9, 2006): 1–15. http://dx.doi.org/10.1093/qmath/hal019.

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45

Seyfarth, S., and M. A. Shubin. "Lefschetz fixed point formula for manifolds with cylindrical ends." Annals of Global Analysis and Geometry 9, no. 2 (1991): 99–108. http://dx.doi.org/10.1007/bf00776849.

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46

Battisti, Ubertino, and Sandro Coriasco. "Wodzicki residue for operators on manifolds with cylindrical ends." Annals of Global Analysis and Geometry 40, no. 2 (May 13, 2011): 223–49. http://dx.doi.org/10.1007/s10455-011-9255-3.

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47

Mrowka, Tomasz, Daniel Ruberman, and Nikolai Saveliev. "An index theorem for end-periodic operators." Compositio Mathematica 152, no. 2 (September 7, 2015): 399–444. http://dx.doi.org/10.1112/s0010437x15007502.

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Анотація:

We extend the Atiyah, Patodi, and Singer index theorem for first-order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes’ Fredholm theory for general end-periodic operators. Our index theorem is expressed in terms of a new periodic eta-invariant that equals the Atiyah–Patodi–Singer eta-invariant in the cylindrical setting. We apply this periodic eta-invariant to the study of moduli spaces of Riemannian metrics of positive scalar curvature.

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48

Hunsicker, E. "Extended Hodge theory for fibred cusp manifolds." Journal of Topology and Analysis 10, no. 03 (August 30, 2018): 531–62. http://dx.doi.org/10.1142/s1793525318500188.

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For a particular class of pseudo manifolds, we show that the intersection cohomology groups for any perversity may be naturally represented by extended weighted [Formula: see text] harmonic forms for a complete metric on the regular stratum with respect to some weight determined by the perversity. Extended weighted [Formula: see text] harmonic forms are harmonic forms that are almost in the given weighted [Formula: see text] space for the metric in question, but not quite. This result is akin to the representation of absolute and relative cohomology groups for a manifold with boundary by extended harmonic forms on the associated manifold with cylindrical ends. In analogy with that setting, in the unweighted [Formula: see text] case, the boundary values of the extended harmonic forms define a Lagrangian splitting of the boundary space in the long exact sequence relating upper and lower middle perversity intersection cohomology groups.

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49

Taniguchi, Masaki. "Instantons for 4-manifolds with periodic ends and an obstruction to embeddings of 3-manifolds." Topology and its Applications 243 (July 2018): 1–32. http://dx.doi.org/10.1016/j.topol.2018.04.016.

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50

Avramidi, Grigori, and T. Tâm Nguyễn-Phan. "Half-dimensional collapse of ends of manifolds of nonpositive curvature." Geometric and Functional Analysis 29, no. 6 (November 16, 2019): 1638–702. http://dx.doi.org/10.1007/s00039-019-00515-2.

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Анотація:

AbstractThis paper accomplishes two things. First, we construct a geometric analog of the rational Tits building for general noncompact, complete, finite volume n-manifolds M of bounded nonpositive curvature. Second, we prove that this analog has dimension less than $$\lfloor n/2\rfloor $$⌊n/2⌋.

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