Foliated Positive Scalar Curvature

von Jialong Deng
Dissertation
Datum der mündl. Prüfung:2021-10-07
Erschienen:2021-11-11
Betreuer:Prof. Dr. Thomas Schick
Gutachter:Prof. Dr. Thomas Schick
Gutachter:Prof. Dr. Viktor Pidstrygach
Zum Verlinken/Zitieren: http://dx.doi.org/10.53846/goediss-8930

 

 

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Zusammenfassung

Englisch

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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