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Regularity of isoperimetric hypersurfaces in Riemannian manifolds

Author(s): Frank Morgan
Journal: Trans. Amer. Math. Soc. 355 (2003), 5041-5052.
MSC (2000): Primary 49Q20
Posted: July 28, 2003
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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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Additional Information:

Frank Morgan
Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
Email: Frank.Morgan@williams.edu

DOI: 10.1090/S0002-9947-03-03061-7
PII: S 0002-9947(03)03061-7
Keywords: Isoperimetric hypersurface, area-minimizing, fixed volume, regularity, Lipschitz metric, constant mean curvature
Received by editor(s): December 12, 2001
Received by editor(s) in revised form: March 27, 2002 and October 18, 2002
Posted: July 28, 2003
Copyright of article: Copyright 2003, by the author

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