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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Isoperimetric regions in cones


Authors: Frank Morgan and Manuel Ritoré
Journal: Trans. Amer. Math. Soc. 354 (2002), 2327-2339
MSC (2000): Primary 53C42; Secondary 49Q20
Published electronically: February 12, 2002
MathSciNet review: 1885654
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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: http://dx.doi.org/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
Published electronically: February 12, 2002
Article copyright: © Copyright 2002 by the authors