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.
Citation
James J. Hebda. Yutaka Ikeda. "Necessary and sufficient conditions for a triangle comparison theorem." Tohoku Math. J. (2) 74 (3) 329 - 364, 2022. https://doi.org/10.2748/tmj.20210215
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