Geodesic
Obata’s Rigidity Theorem for Metric Measure Spaces
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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.
Mots-clés : eigenvalue, suspension, Hessian, convexity 
@article{AGMS_2015_3_1_a7,
     author = {Ketterer, Christian},
     title = {Obata{\textquoteright}s {Rigidity} {Theorem} for {Metric} {Measure} {Spaces}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     zbl = {1327.53051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a7/}
}
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Ketterer, Christian. Obata’s Rigidity Theorem for Metric Measure Spaces. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a7/