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| 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 $K_u(X_2)$. |
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| Keywords:Gromov hyperbolic space; Asymptotic upper curvature bound; Hyperbolic product |
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