Results 31 to 40 of about 193,577 (332)
Michigan Mathematical Journal, 1998 The study of relatively hyperbolic groups (that is, hyperbolicity of a group relative to a family of subgroups) is motivated by the following situation: let \(V\) be a complete noncompact Riemannian manifold of constant negative curvature with finite volume. Then \(V\) has finitely many ends \(E_1,\dots,E_k\), and the inclusions \(E_i\subset V\) induce
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Hyperbolic boundaries vs. hyperbolic groups
, 2022 These notes are based on lectures given by the third author at CIRM in the Summer of ...
Ben-Zvi, Michael +2 more
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Relative Hyperbolicity and Artin Groups [PDF]
Geometriae Dedicata, 2004 Let $G=$ be an Artin group and let $m_{ij}=m_{ji}$ be the length of each of the sides of the defining relation involving $a_i$ and $a_j$. We show if all $m_{ij}\ge 7$ then $G$ is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups $$ for which $m_{ij}
Kapovich, Ilya, Schupp, Paul
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Type-I hyperbolic metasurfaces for highly-squeezed designer polaritons with negative group velocity
Nature Communications, 2019 Hyperbolic polaritons provide unprecedented control over light-matter interaction at extreme nanoscales. Here, the authors propose type-I hyperbolic metasurfaces supporting highly-squeezed magnetic designer polaritons with negative group velocity, which ...
Yihao Yang +6 more
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On the boundedness of invariant hyperbolic domains
Comptes Rendus. Mathématique, 2020 In this paper, we generalize a theorem of A. Kodama about boundedness of hyperbolic circular domains. We will prove that if $K$ is a compact Lie group which acts linearly on $\mathbb{C}^n$ with $\mathcal{O}(\mathbb{C}^n)^K=\mathbb{C}$, and $\Omega $ is a
Ning, Jiafu, Zhou, Xiangyu
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COMPLEX OF RELATIVELY HYPERBOLIC GROUPS [PDF]
Glasgow Mathematical Journal, 2018 AbstractIn this paper, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin’s (Geom. Topology 18 (2014), 31–102) work for combination of hyperbolic groups over a finite MK-simplicial complex, where k ≤ 0.
Pal, Abhijit, Paul, Suman
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Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity [PDF]
, 2008 We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral ...
Behrstock, Jason +2 more
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Faithful real representations of cyclically pinched one-relator groups [PDF]
International Journal of Group Theory, 2014 In [FR 1,2] using faithful complex representations of cyclically pinched andconjugacy pinched one-relator groups we proved that any limit group has afaithful representation in PSL(2;C). Further this representation can be e ec-tively constructed using the
Benjamin Fine +2 more
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Inverse Numerical Range and Determinantal Quartic Curves
Mathematics, 2020 A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range ...
Mao-Ting Chien, Hiroshi Nakazato
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Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups
Abstract and Applied Analysis, 2014 We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if the r-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group.
Huani Qin, Yueping Jiang, Wensheng Cao
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