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

Shing-Tung Yau
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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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Shing-Tung Yau. 2002-02-28. Geometry of three manifolds and existence of Black Hole due to boundary effect. https://arxiv.org/abs/math/0109053

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