English

Geometry of three manifolds and existence of Black Hole due to boundary effect

Differential Geometry 2007-05-23 v2

Abstract

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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Cite

@article{arxiv.math/0109053,
  title  = {Geometry of three manifolds and existence of Black Hole due to boundary effect},
  author = {Shing-Tung Yau},
  journal= {arXiv preprint arXiv:math/0109053},
  year   = {2007}
}

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