Geometry of three manifolds and existence of Black Hole due to boundary effect
Shing-Tung Yau
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.
Create a lesson
Related papers
The Bernstein problem in higher dimensional Heisenberg groups
Gianmarco Giovannardi, Simone Verzellesi
A Lean Formalization of the Hamilton--Perelman Proof of Thurston's Geometrization Conjecture
Yuan Liao, Ziyang Qin, Jui-Hui Chung et al.
A counterexample to Nirenberg's conjecture on closed asymptotic curves
Harrison Banks, Mohammad Ghomi, Hongda Qiu et al.
Topping's conjecture for solutions of harmonic map flow with isolated bubbles
Melanie Rupflin, Alex Waldron, Sebastian Woodward
The Renormalized Area--Willmore Relation
Alvaro Pampano, Aaron J. Tyrrell
Compact lcK manifolds with Gauduchon parallel vector fields
Andrei Moroianu, Giacomo Perri