Obata’s Rigidity Theorem for Metric Measure Spaces
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2015-10-01
|
| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2015-0016 |
| Summary: | 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. |
|---|---|
| ISSN: | 2299-3274 |