The Injectivity Radius of Souls of Alexandrov Spaces

Elena Mäder-Baumdicker, Jona Seidel

Published 2023-10-05Version 1

We generalize a sharp lower bound of the injectivity radius in noncompact nonnegatively curved Riemannian manifolds found by \v{S}arafutdinov to the setting of Alexandrov spaces. The injectivity radius either coincides with that of souls or is not less than $ \pi K^{-1/2} $, where $ K $ is an upper curvature bound. We give an introduction to the theory of the soul of Alexandrov spaces and compare two injectivity radii.