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arXiv · 1806.04633

Necessary and Sufficient Conditions for a Triangle Comparison Theorem

James J. Hebda·Yutaka Ikeda
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Abstract

We prove a version of Topogonov's triangle comparison theorem with surfaces of revolution as model spaces. Given a model surface and a Riemannian manifold with a fixed base point, we give necessary and sufficient conditions under which every geodesic triangle in the manifold with a vertex at the base point has a corresponding Alexandrov triangle in the model. Under these conditions we also prove a version of the Maximal Radius Theorem and a Grove--Shiohama type Sphere Theorem.

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James J. Hebda, Yutaka Ikeda. 2018-06-12. Necessary and Sufficient Conditions for a Triangle Comparison Theorem. https://arxiv.org/abs/1806.04633

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