A Remark on Almost Umbilical Hypersurfaces
Julien Roth (LAMA)
TL;DR
This paper establishes new stability results for almost-Einstein and almost umbilical hypersurfaces in Euclidean space, leveraging eigenvalue pinching techniques to derive geometric conclusions.
Contribution
It introduces novel stability results for almost-Einstein hypersurfaces and extends these findings to almost umbilical hypersurfaces, based on eigenvalue pinching methods.
Findings
Stability results for almost-Einstein hypersurfaces
Comparable results for almost umbilical hypersurfaces
Use of eigenvalue pinching techniques
Abstract
In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research