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Transactions of the American Mathematical Society

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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: 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: 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

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