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Isoperimetric regions in cones

Author(s): Frank Morgan; Manuel Ritoré
Journal: Trans. Amer. Math. Soc. 354 (2002), 2327-2339.
MSC (2000): Primary 53C42; Secondary 49Q20
Posted: February 12, 2002
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Abstract: We consider cones $C = 0\, \times{\kern-10.5pt}\times \,M^n$ and prove that if the Ricci curvature of $C$ is nonnegative, then geodesic balls about the vertex minimize perimeter for given volume. If strict inequality holds, then they are the only stable regions.

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Additional Information:

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

Manuel Ritoré
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, E--18071 Granada, España
Email: ritore@ugr.es

DOI: 10.1090/S0002-9947-02-02983-5
PII: S 0002-9947(02)02983-5
Received by editor(s): May 23, 2001
Received by editor(s) in revised form: November 1, 2001
Posted: February 12, 2002
Copyright of article: Copyright 2002, by the authors

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