共查询到20条相似文献,搜索用时 15 毫秒
1.
K. Bromberg 《Geometriae Dedicata》2004,105(1):143-170
In a recent paper Hodgson and Kerckhoff prove a local rigidity theorem for finite volume, three-dimensional hyperbolic cone-manifolds.
In this paper we extend this result to geometrically finite cone-manifolds. Our methods also give a new proof of a local version
of the classical rigidity theorem for geometrically finite hyperbolic 3-manifolds. 相似文献
2.
By using Klein??s model for hyperbolic geometry, hyperbolic structures on orbifolds or manifolds provide examples of real projective structures. By Andreev??s theorem, many 3-dimensional reflection orbifolds admit a finite volume hyperbolic structure, and such a hyperbolic structure is unique. However, the induced real projective structure on some such 3-orbifolds deforms into a family of real projective structures that are not induced from hyperbolic structures. In this paper, we find new classes of compact and complete hyperbolic reflection 3-orbifolds with such deformations. We also explain numerical and exact results on projective deformations of some compact hyperbolic cubes and dodecahedra. 相似文献
3.
Muharem Avdispahi 《Mathematische Nachrichten》2019,292(4):691-693
We correct the exponent in the error term of the prime geodesic theorem for hyperbolic 3‐manifolds 1 and in Park's theorem for higher dimensions [ 3 , 2 ]. 相似文献
4.
Shuxing Chen 《Frontiers of Mathematics in China》2007,2(1):87-102
This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic
boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. The
concept on regular characteristics and dissipative boundary conditions are given for quasilinear hyperbolic systems. Under
some assumptions, an existence theorem for such initial boundary value problems is obtained. The theorem can also be applied
to the Euler system of compressible flow.
__________
Translated from Chinese Annals of Mathematics, Ser. A, 1982, 3(2): 223–232 相似文献
5.
Daniel Maerten 《Annales Henri Poincare》2006,7(5):975-1011
The aim of this paper is to prove a positive energy-momentum theorem under the (well known in general relativity) dominant
energy condition, for AdS-asymptotically hyperbolic manifolds. These manifolds are by definition endowed with a Riemannian
metric and a symmetric 2-tensor which respectively tend to the metric and second fundamental form of a standard hyperbolic
slice in Anti-de Sitter space-time. There exists a positive mass theorem for asymptotically hyperbolic spin Riemannian manifolds
(with zero extrinsic curvature), and we present an extension of this result for the non zero extrinsic curvature case.
Communicated by Sergiu Klainerman
Submitted: January 15, 2006 Accepted: January 15, 2006 相似文献
6.
Quasi—Einstein Hypersurfaces in a Hyperbolic Space 总被引:1,自引:0,他引:1
§1. IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj, (i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1… 相似文献
7.
Marc Lackenby 《Geometriae Dedicata》2010,147(1):191-206
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-volume hyperbolic 3-manifold
M, in terms of data from any surgery diagram for M. This has several consequences. We prove that a family of hyperbolic alternating link complements is expanding if and only
if they have bounded volume. We also provide examples of hyperbolic 3-manifolds which require ‘complicated’ surgery diagrams,
thereby proving that a recent theorem of Constantino and Thurston is sharp. Along the way, we find a new upper bound on the
bridge number of a knot that is not tangle composite, in terms of the twist number of any diagram of the knot. The proofs
rely on a theorem of Lipton and Tarjan on planar graphs, and also the relationship between many different notions of width
for knots and 3-manifolds. 相似文献
8.
Teruhiko Soma 《Transactions of the American Mathematical Society》2006,358(9):4057-4070
We will present a new proof of the rigidity theorem for Seifert fibered spaces of infinite by Scott (1983) in the case when the base of the fibration is a hyperbolic triangle 2-orbifold. Our proof is based on arguments in the rigidity theorem for hyperbolic 3-manifolds by Gabai (1997).
9.
Xiangdong Xie 《Mathematische Zeitschrift》2008,259(2):249-253
We establish a Bowen type rigidity theorem for the fundamental group of a noncompact hyperbolic manifold of finite volume
(with dimension at least 3).
相似文献
10.
本文的主要定理是:对每一个正数V,存在一个D>0,如果一个3维黎曼流形M的体积小于V,截面曲率在-1和0之间,而且直径大于D,那么M允许一个双曲结构。 相似文献
11.
We show that the open unit ball of the space of operators from a finite-dimensional Hilbert space into a separable Hilbert space (we call it “operator ball”) has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of the standard hyperbolic metric on the unit disc in the complex plane). We use this result to get a fixed point theorem for groups of biholomorphic automorphisms of the operator ball. The fixed point theorem is used to show that a bounded representation in a separable Hilbert space which has an invariant indefinite quadratic form with finitely many negative squares is unitarizable (equivalent to a unitary representation). We apply this result to find dual pairs of invariant subspaces in Pontryagin spaces. In Appendix A we present results of Itai Shafrir about hyperbolic metrics on the operator ball. 相似文献
12.
本文证明了双曲空间中的共形平坦极小超曲面必为旋转超曲面或由一些旋转超曲面片用全测地超曲面片粘合而成.将这结果与王新民及许志才的一个已发表定理相组合,推广了Blair关于推广悬链面的一个定理. 相似文献
13.
Rolf Struve 《Results in Mathematics》2014,66(3-4):363-366
Knüppel (J Geom 105:13–20, 2014) shows that in a hyperbolic plane an asymptotic n-gon does not admit a transversal line when n is odd. If n is even then there exist n-gons which admit a transversal line. Recently Struve (J Geom 103:333–346, 2012) showed that in hyperbolic geometry an order structure can be introduced purely in terms of the calculus of reflections. Following this approach we give a short proof of the above mentioned theorem which provides new insights into the underlying foundations of the theorem. 相似文献
14.
本文给出了关于哈密顿系统低维环面的一个推广的KAM定理,它适用于同时存在法向频率和双曲法向分量的情况.其证明基于尤建功的一个定理的光滑性表述及法向双曲不变流形理论的应用.文中还给出了另外两种情况下的推广. 相似文献
15.
The Witten spinorial argument has been adapted in several works over the years to prove positivity of mass in the asymptotically
AdS and asymptotically hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar curvature rigidity result
and a positive mass theorem for asymptotically hyperbolic manifolds that do not require a spin assumption. The positive mass
theorem is reduced to the rigidity case by a deformation construction near the conformal boundary. The proof of the rigidity
result is based on a study of minimizers of the BPS brane action.
Submitted: March 16, 2007. Accepted: June 14, 2007. 相似文献
16.
B.C. Dhage 《Journal of Mathematical Analysis and Applications》2007,335(1):225-242
In this paper, an existence theorem for a certain hyperbolic differential inclusions in Banach algebras is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions for Carathéodory as well as discontinuous hyperbolic differential inclusions is also proved under certain monotonicity conditions. 相似文献
17.
In this paper, a q uniqueness theorem is proved for a hyperbolic boundary problem with data on the characteristic cone. 相似文献
18.
According to the planar version of Ivory's theorem, the family of confocal conics has the property that in each curvilinear quadrangle formed by two pairs of conics the diagonals are of equal length. It turned out that this theorem is closely related to selfadjoint affine transformations. This point of view opens up a possibility of generalizing the Ivory theorem to the hyperbolic and other spaces. 相似文献
19.
J. Tölke 《Geometriae Dedicata》2001,84(1-3):35-39
We prove a hyperbolic analogon of the euclidean theorem of Abramescu. The proof makes use of the basic concepts of plane hyperbolic differential geometry of G. W. M. Kallenberg. 相似文献
20.
G. Farkas 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2001,6(1):421-432
A weak form of the Hartman-Grobman theorem for retarded functional differential equations around hyperbolic equilibria is presented. Orbits on a center-unstable manifold are compared to orbits on a center-unstable subspace of the linearized equation. The result is applied to obtain a conjugacy between the semidynamical system generated by the functional differential equation and its numerical approximation. A version of the Hartman-Grobman theorem around hyperbolic periodic orbits of functional differential equations is also given. 相似文献