Quantitative Obata's Theorem
Functional Analysis
2023-08-30 v3 Differential Geometry
Metric Geometry
Abstract
We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise. These results are obtained in the general framework of (possibly non-smooth) metric measure spaces with curvature-dimension conditions through a quantitative analysis of the transport-rays decompositions obtained by the localization method.
Cite
@article{arxiv.1910.06637,
title = {Quantitative Obata's Theorem},
author = {Fabio Cavalletti and Andrea Mondino and Daniele Semola},
journal= {arXiv preprint arXiv:1910.06637},
year = {2023}
}
Comments
38 pages. Final version to appear in Analysis and PDEs