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 hepth/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:

arXiv Mathematics eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:math/0109053
 Bibcode:
 2001math......9053Y
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 LaTeX 12 pages