Sphere theorems for RCD and stratified spaces
Shouhei Honda, Ilaria Mondello
TL;DR
This paper establishes topological sphere theorems for RCD spaces, extending classical results to a broader geometric setting and improving outcomes for Einstein stratified spaces.
Contribution
It generalizes classical sphere theorems to RCD spaces and enhances results for Einstein stratified spaces.
Findings
Proved topological sphere theorems for RCD(n-1, n) spaces
Extended Colding's and Petersen's results to the RCD setting
Improved sphere theorem for Einstein stratified spaces
Abstract
We prove topological sphere theorems for RCD(n-1, n) spaces which generalize Colding's results and Petersen's result to the RCD setting. We also get an improved sphere theorem in the case of Einstein stratified spaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research