# 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.

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