Structure of Manifolds with Positive Curvature Based on Geometric Analysis

Shing-Tung Yau

Geometric Analysis and Geometric Topology mathscidoc:1912.43715

Notices of the International Congress of Chinese Mathematicians, 1, (2), 24-28, 2013.12
The Gauss-Bonnet theorem and the Cohn-Vossen inequality show that the only complete surface with positive curvature is either the sphere, RP2, or the plane. In higher dimension, the curvature tensor is far more complicated. There are several commonly used partial components of the curvature tensor that had been studied for the whole century. The simplest one is the scalar curvature which is the average of all curvatures at one point. It appeared in the Hilbert action for general relativity. This was studied extensively in connection with general relativity.
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@inproceedings{shing-tung2013structure,
  title={Structure of Manifolds with Positive Curvature Based on Geometric Analysis},
  author={Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205158267677279},
  booktitle={Notices of the International Congress of Chinese Mathematicians},
  volume={1},
  number={2},
  pages={24-28},
  year={2013},
}
Shing-Tung Yau. Structure of Manifolds with Positive Curvature Based on Geometric Analysis. 2013. Vol. 1. In Notices of the International Congress of Chinese Mathematicians. pp.24-28. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205158267677279.
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