Quantitative Obata's Theorem

Author: 

Cavalletti, F
Mondino, A
Semola, D

Publication Date: 

15 October 2019

Journal: 

arXiv

Last Updated: 

2020-07-24T00:49:20.983+01:00

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.

Symplectic id: 

1070572

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article