Foliated Positive Scalar Curvature

by Jialong Deng
Doctoral thesis
Date of Examination:2021-10-07
Date of issue:2021-11-11
Advisor:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Viktor Pidstrygach
Persistent Address: http://dx.doi.org/10.53846/goediss-8930

 

 

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Abstract

English

In this thesis we study different questions on scalar curvatures. The first part is devoted to obstructions against existence of a (Riemannian) metric with positive scalar curvature on a closed manifold. The second part investigates the synthetic definition of scalar curvature bounded below on metric measure spaces. In the third and fourth part, we define and study weighted scalar curvature on a smooth metric measure space. We show rigidity results about scalar curvature bounded below and a sphere theorem for RCD(n-1; n) spaces in the final part.
Keywords: Obstructions; Weighted scalar curvature; Rigidity results
 
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