Year: 2024
Type: article
Abstract: A sharp lower bound for the injectivity radius in noncompact nonnegatively curved Riemannian manifolds involving their soul goes back to Šarafutdinov. We generalize this bound to the setting of Alexandrov spaces. Our main theorem reads as follows. If the injectivity radius of an Alexandrov space of nonnegative curvature does not coincide with the one of its souls, then it is at least $$ \pi K^{-1/2} $$ π K - 1 / 2 , where K is an upper curvature bound. We introduce the soul of Alexandrov spaces in some detail and compare two notions of injectivity radii.
Source: Journal of Geometric Analysis
Authors: Elena Mäder-Baumdicker, Jona Seidel
Institution: Technische Universität Darmstadt
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G2344767758, G4719459919
OpenAlex ID: W4405274285