Calculus of Variations and Geometric Measure Theory

S. Honda - A. Mondino

Gap phenomena under curvature restrictions

created by mondino on 08 Oct 2024
modified on 28 Mar 2025

[BibTeX]

Accepted Paper

Inserted: 8 oct 2024
Last Updated: 28 mar 2025

Journal: Indagationes Math.
Year: 2025

ArXiv: 2410.04985 PDF

Abstract:

In the paper we discuss gap phenomena of three different types related to Ricci (and sectional) curvature. The first type is about \textit{spectral gaps}. The second type is about \textit{sharp gap metric-rigidity}, originally due to Anderson. The third is about \textit{sharp gap topological-rigidity}. We also propose open problems along these directions.


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