Mathematical Research Letters

Volume 12 (2005)

Number 2

The Existence of Horizons in an Asymptotically Flat 3-Manifold

Pages: 219 – 230



Yu Yan (The University of British Columbia)


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

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