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 nonsmooth) metric measure spaces with curvature-dimension conditions through a quantitative analysis of the transport-ray decompositions obtained by the localization method.
Quantitative Obata’s theorem / F. Cavalletti, A. Mondino, D. Semola. - In: ANALYSIS & PDE. - ISSN 1948-206X. - 16:6(2023 Aug 23), pp. 1389-1431. [10.2140/apde.2023.16.1389]
Quantitative Obata’s theorem
F. Cavalletti
Primo
;
2023
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 nonsmooth) metric measure spaces with curvature-dimension conditions through a quantitative analysis of the transport-ray decompositions obtained by the localization method.File | Dimensione | Formato | |
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