Rigidity of the spectral gap for non-negatively curved RCD spaces
07.12. bis 07.12.2021, 12:15-13:45
– room C9A03 Tübingen, room 2.09.2.22 Golm
Geometric Analysis, Differential Geometry and Relativity
Christian Ketterer
Rigidity of the spectral gap for non-negatively curved RCD spaces
First I will review results about the connection between spectral estimates and Ricci curvature for Riemannian manifolds and metric measure spaces. In particular for non-negatively curved spaces the spectral gap is $(\pi/diam)^2$. Moreover, an RCD(0,N) space has first Laplace eigenvalue equal to $(\pi/diam)^2$ if and only if it is a circle or an interval. This is joint work with Yu Kitabeppu and Sajjad Lakzian.