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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 1, 2015

Obata’s Rigidity Theorem for Metric Measure Spaces

  • Christian Ketterer


We prove Obata’s rigidity theorem for metric measure spaces that satisfy a Riemannian curvaturedimension condition. Additionally,we show that a lower bound K for the generalizedHessian of a sufficiently regular function u holds if and only if u is K-convex. A corollary is also a rigidity result for higher order eigenvalues.


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Received: 2015-3-1
Accepted: 2015-8-25
Published Online: 2015-10-1

© 2015 Christian Ketterer

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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