Regularity of isoperimetric hypersurfaces in Riemannian manifolds

Morgan, Frank

doi:10.1090/S0002-9947-03-03061-7

Regularity of isoperimetric hypersurfaces in Riemannian manifolds
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Trans. Amer. Math. Soc. 355 (2003), 5041-5052

Abstract:

We add to the literature the well-known fact that an isoperimetric hypersurface $S$ of dimension at most six in a smooth Riemannian manifold $M$ is a smooth submanifold. If the metric is merely Lipschitz, then $S$ is still Hölder differentiable.

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