Geometry of three manifolds and existence of Black Hole due to boundary effect
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- September 2001
- DOI:
- 10.48550/arXiv.math/0109053
- arXiv:
- arXiv:math/0109053
- Bibcode:
- 2001math......9053Y
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- LaTeX 12 pages