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

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

2001-09-07

arxiv.org/abs/math/0109053v2

Mathematics

Differential Geometry

LaTeX 12 pages

Scientific paper

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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