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タイトル: Growth and cogrowth tightness of Kleinian and hyperbolic groups (Geometry and Analysis of Discrete Groups and Hyperbolic Spaces)
著者: Matsuzaki, Katsuhiko
著者名の別形: 松崎, 克彦
キーワード: 37C35
30F40
53C23
20F65
57S30
37D40
growth tight
Kleinian group
critical exponent
volume entropy
Gromov hyperbolic space
quasi-convex cocompact
発行日: Jun-2017
出版者: Research Institute for Mathematical Sciences, Kyoto University
誌名: 数理解析研究所講究録別冊
巻: B66
開始ページ: 21
終了ページ: 36
抄録: Let G be a non-elementary discrete isometry group of the hyperbolic space or more generally a proper geodesic Gromov hyperbolic space X. We say that G is growth tight if for any non-trivial normal subgroup H the critical exponent k(H\G) of the quotient group is strictly smaller than k(G). Moreover, G is cogrowth tight if the critical exponent δ(H) of any such H is strictly greater than δ(G)/2. We review recent results on these properties of G with the addition of certain new observation. In particular, we see that a non-elementary quasi-convex cocompact discrete isometry group G of X is growth tight.
記述: "Geometry and Analysis of Discrete Groups and Hyperbolic Spaces". June 22~26, 2015. edited by Michihiko Fujii, Nariya Kawazumi and Ken'ichi Ohshika. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
著作権等: © 2017 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
URI: http://hdl.handle.net/2433/243691
出現コレクション:B66 Geometry and Analysis of Discrete Groups and Hyperbolic Spaces

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