Communications in Analysis and Geometry

Volume 16 (2008)

Number 4

Existence of outermost apparent horizons with product of spheres topology

Pages: 799 – 817



Fernando Schwartz (Duke University)


In this paper we construct the first examples of $(n+m+2)$-dimensional asymptotically flat Riemannian manifolds withnon-negative scalar curvature that have outermost minimalhypersurfaces with non-spherical topology for $n,m\ge 1$.

The outermost minimal hypersurfaces are, topologically,$S^n\times S^{m+1}$. In the context of general relativitythese hypersurfaces correspond to outermost apparenthorizons of black holes.

Published 1 January 2008