Strongly Contracting Geodesics in a Tree of Spaces

Abhijit Pal; Suman Paul

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arXiv · 1904.09906

Strongly Contracting Geodesics in a Tree of Spaces

Abhijit Pal·Suman Paul

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Abstract

Let X be a tree of proper geodesic spaces with edge spaces strongly contracting and uniformly separated from each other by a number depending on the contraction function of edge spaces. Then we prove that the strongly contracting geodesics in vertex spaces are quasiconvex in X. We further prove that in X if all the vertex spaces are uniformly hyperbolic metric spaces then X is a hyperbolic metric space and vertex spaces are quasiconvex in X.

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Abhijit Pal, Suman Paul. 2019-04-22. Strongly Contracting Geodesics in a Tree of Spaces. https://arxiv.org/abs/1904.09906

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