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Homotopy hyperbolic 3-manifolds are hyperbolic [PDF]
Annals of Mathematics, 2003 This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This technique is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold.
Gabai, David +2 more
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Harmonic maps into hyperbolic 3-manifolds [PDF]
Transactions of the American Mathematical Society, 1992 High-energy degeneration of harmonic maps of Riemann surfaces into a hyperbolic 3 3 -manifold target is studied, generalizing results of [M1] in which the target is two-dimensional. The Hopf foliation of a high-energy map is mapped to an approximation of its geodesic representative in the target, and the ratio of the squared length of ...
Yair N. Minsky
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Dehn filling hyperbolic 3-manifolds [PDF]
Pacific Journal of Mathematics, 1994 Define a complete family of parent (ancestor) manifolds to be a set of compact 3-manifolds such that every closed orientable 3-manifold can be obtained by one (or more) Dehn fillings of the manifolds in the family. In 1983, R. Myers proved that the set of 1-cusped hyperbolic 3-manifolds is a complete family of parent manifolds.
Colin Adams
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Simple Closed Geodesics in Hyperbolic 3-Manifolds [PDF]
Bulletin of the London Mathematical Society, 1999 This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only example of a complete non-elementary orientable hyperbolic 3-manifold that does not contain a simple closed geodesic. We do not assume that the manifold is geometrically finite
Colin Adams, Joel Hass, Peter Scott
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Riemann solitons on para-Sasakian geometry
Karpatsʹkì Matematičnì Publìkacìï, 2022 The goal of the present article is to investigate almost Riemann soliton and gradient almost Riemann soliton on 3-dimensional para-Sasakian manifolds.
K. De, U.C. De
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Black holes and large N complex saddles in 3D-3D correspondence
Journal of High Energy Physics, 2021 We study the large N sign oscillation of the twisted indices for 3D theories of class ℛ obtained from M5-branes wrapped on a hyperbolic 3-manifold. Holographically, the oscillatory behavior can be understood from the imaginary part of on-shell actions ...
Sunjin Choi, Dongmin Gang, Nakwoo Kim
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Infrared phases of 3D class R theories
Journal of High Energy Physics, 2022 We study the IR phases of 3D class R theories associated with closed non-hyperbolic 3-manifolds. Non-hyperbolic 3-manifolds can be obtained by performing Dehn fillings on 1-cusped hyperbolic 3-manifolds along exceptional slopes.
Sunjin Choi, Dongmin Gang, Hee-Cheol Kim
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Journal of High Energy Physics, 2020 We study the twisted index of 4d N $$ \mathcal{N} $$ = 2 class S $$ \mathcal{S} $$ theories on a closed hyperbolic 3-manifold M 3. Via 6d picture, the index can be written in terms of topological invariants called analytic torsions twisted by irreducible
Jin-Beom Bae, Dongmin Gang, Kimyeong Lee
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Hardy–Adams Inequalities on ℍ2 × ℝn-2
Advanced Nonlinear Studies, 2021 Let ℍ2{\mathbb{H}^{2}} be the hyperbolic space of dimension 2. Denote by Mn=ℍ2×ℝn-2{M^{n}=\mathbb{H}^{2}\times\mathbb{R}^{n-2}} the product manifold of ℍ2{\mathbb{H}^{2}} and ℝn-2(n≥3){\mathbb{R}^{n-2}(n\geq 3)}.
Ma Xing, Wang Xumin, Yang Qiaohua
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Bloch invariants of hyperbolic 3-manifolds [PDF]
Duke Mathematical Journal, 1999 25 pages. A slightly revised version will appear in Duke Math. J.
Neumann, Walter D., Yang, Jun
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