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1. On the Asymptotic upper curvature of hyperbolic products | |||
XIE Gui-Ling,XIAO Ying-Qing | |||
Mathematics 15 May 2017 | |||
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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 $K_u(X_2)$. | |||
TO cite this article:XIE Gui-Ling,XIAO Ying-Qing. On the Asymptotic upper curvature of hyperbolic products[OL].[15 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733628 |
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