Positive Scalar Curvature: Existence and Rigidity

Time：2023-11-28 Tue 14:30-15:30

Venue：A3-4-301 ZOOM: 928 682 9093（PW: BIMSA）

Organizer：Lynn Heller, Sebastian Heller, Kotaro Kawai

Speaker：Jialong Deng Tsinghua University

Abstract

The scalar curvature of a Riemannian metric is interesting not only in analysis, geometry, and topology, but also in physics. Enlargeable Length-structures will be introduced and showed that it is a new obstruction to the existence of a Riemannian metric with positive scalar curvature (PSC-metric). Thus, the connected sum of a closed manifold with some of locally CAT(0)-manifolds carry not PSC-metrics. We will also show that almost non-positive curved manifolds carry no PSC-metrics. On the other hand, harmonic maps with condition C will be used to show the rigidity theorem about the scalar curvature.

DATENovember 28, 2023

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