The existence of horizons in an asymptotically flat 3-manifold

摘要

In this paper we study the type of asymptotically flat manifolds of the form (S-3 {P}, G(4)g), where G is a Green's function of the conformal Laplacian of (S3, g) at P. We give a sufficient condition on the background metric g which guarantees the existence of a minimal surface in (S-3 {P}, G(4)g).