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Geometry of three manifolds and existence of black hole due to boundary effect

Shing-Tung Yau

Differential Geometry mathscidoc:1912.43534

arXiv preprint math/0109053, 2001.9
In this paper, we observe that the brane functional studied in hep-th/9910245 can be used to generalize some of the works that Schoen and I [4] did many years ago. The key idea is that if a three dimensional manifold M has a boundary with strongly positive mean curvature, the effect of this mean curvature can influence the internal geometry of M. For example, if the scalar curvature of M is greater than certain constant related to this boundary effect, no incompressible surface of higher genus can exist.
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@inproceedings{shing-tung2001geometry,
  title={Geometry of three manifolds and existence of black hole due to boundary effect},
  author={Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203849720103098},
  booktitle={arXiv preprint math/0109053},
  year={2001},
}
Shing-Tung Yau. Geometry of three manifolds and existence of black hole due to boundary effect. 2001. In arXiv preprint math/0109053. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203849720103098.
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