Locally Minimizing Smooth Harmonic Maps from Asymptotically Flat Manifolds into Spheres

Boundary Regularity and the Dirichlet Problem for Harmonic Maps

In a previous paper [10] we developed an interior regularity theory for energy minimizing harmonic maps into Riemannian manifolds. In the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed Dirichlet boundary condition. We show that such maps are regular in a full neighborhood of the boundary, assuming appropriate regularity on the manifolds,...

Energy Quantization for Harmonic Maps

In this paper we establish the higher-dimensional energy bubbling results for harmonic maps to spheres. We have shown in particular that the energy density of concentrations has to be the sum of energies of harmonic maps from the standard 2dimensional spheres. The result also applies to the structure of tangent maps of stationary harmonic maps at either a singularity or infinity. 0. Introductio...

Existence of Outermost Apparent Horizons with Product of Spheres Topology

In this paper we find new examples of Riemannian manifolds with nonspherical apparent horizon, in dimensions four and above. More precisely, for any n, m ≥ 1, we construct asymptotically flat, scalar flat Riemannian manifolds containing smooth outermost minimal hypersurfaces with topology Sn × S. In the context of general relativity these hypersurfaces correspond to outermost apparent horizons ...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

On the Uniqueness of the Foliation of Spheres of Constant Mean Curvature in Asymptotically Flat 3-manifolds

Abstract. In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that there is a unique foliation of stable spheres of constant mean curvature in an asymptotically ...