Obata’s Rigidity Theorem for Metric Measure Spaces

By C. Ketterer. 2014

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Abstract 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.

View Paper: https://www.semanticscholar.org/paper/65b1f0b7f26a37d2355982af5d33d3f58f363f5d