Obata's rigidity theorem for metric measure spaces
Metric Geometry
2015-10-30 v3 Differential Geometry
Abstract
We prove Obata's rigidity theorem for metric measure spaces that satisfy a Riemannian curvature-dimension condition. Additionally, we show that a lower bound for the generalized Hessian of a sufficiently regular function holds if and only if is -convex. A corollary is also a rigidity result for higher order eigenvalues.
Cite
@article{arxiv.1410.5210,
title = {Obata's rigidity theorem for metric measure spaces},
author = {Christian Ketterer},
journal= {arXiv preprint arXiv:1410.5210},
year = {2015}
}
Comments
Theorem 6.1 (Corollary 6.2) is not needed anymore for the proof. Corollary 6.2 has become Corollar 5.4. A rigidity result concerning higher eigenvalues has been added. 20p. Comments are welcome