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Necessary and Sufficient Conditions for a Triangle Comparison Theorem, I

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James Hebda, SLU

  • Geometry/ Topology Seminar
When Tue, Apr 24, 2018
from 03:10 PM to 04:00 PM
Where 231 Ritter Hall
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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 present two topological applications.

This is joint work with Yutaka Ikeda.

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