Regularity of isoperimetric hypersurfaces in Riemannian manifolds

Author:
Frank Morgan

Journal:
Trans. Amer. Math. Soc. **355** (2003), 5041-5052

MSC (2000):
Primary 49Q20

DOI:
https://doi.org/10.1090/S0002-9947-03-03061-7

Published electronically:
July 28, 2003

MathSciNet review:
1997594

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Abstract | References | Similar Articles | Additional Information

Abstract: We add to the literature the well-known fact that an isoperimetric hypersurface of dimension at most six in a smooth Riemannian manifold is a smooth submanifold. If the metric is merely Lipschitz, then 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:
https://doi.org/10.1090/S0002-9947-03-03061-7

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

Published electronically:
July 28, 2003

Article copyright:
© Copyright 2003
by the author