On the Asymptotic upper curvature of hyperbolic products
首发时间:2017-05-22
Abstract:M. Bonk and T. Foertsch introduced the notion of asymptotic upper curvature for Gromov hyperbolic spaces and suggested to study the asymptotic upper curvature of hyperbolic products. In this paper, we study these problems and prove that$$K_u(Y_{Delta,o})leqmax{K_u(X_1),K_u(X_2)},$$where $(X_1,o_1),(X_2,o_2)$ are two point Gromov hyperbolic spaces, $Y_{Delta,o}$ is their hyperbolic product and $K_u(X)$ is the asymptotic upper curvature of a hyperbolic space $X$. Moreover, we obtain some extra conditions to sure that $K_u(Y_{Delta,o})$ is no smaller than $K_u(X_2)$.
keywords: Gromov hyperbolic space Asymptotic upper curvature bound Hyperbolic product
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双曲积的渐近上曲率
摘要:M. Bonk和T. Foertsch提出了Gromov双曲空间的渐近上曲率的概念,并提议研究双曲积的渐近上曲率。本文研究了上述问题,证明了$K_u(Y_{Delta,o})leq max{K_u(X_1),K_u(X_2)}$,其中$(X_1,o_1),(X_2,o_2)$ 是两个给定基点的Gromov 双曲空间,$Y_{Delta,o}$是它们的双曲积,$K_u(X)$是双曲空间$X$的渐近上曲率。此外,在一定的条件下我们得到$K_u(Y_{Delta,o})$大于等于$K_u(X_2)$。
关键词: Gromov双曲空间 渐近上曲率 双曲积
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