Gap phenomena under curvature restrictions
arXiv:2410.04985
Abstract
In the paper we discuss gap phenomena of three different types related to Ricci (and sectional) curvature. The first type is about spectral gaps. The second type is about sharp gap metric-rigidity, originally due to Anderson. The third is about sharp gap topological-rigidity. We also propose open problems along these directions.
18 pages, to appear in Indagationes Mathematicae