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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Isoperimetric regions in cones
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by Frank Morgan and Manuel Ritoré PDF
Trans. Amer. Math. Soc. 354 (2002), 2327-2339

Abstract:

We consider cones $C = 0 \smashtimes M^n$ 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
  • Received by editor(s): May 23, 2001
  • Received by editor(s) in revised form: November 1, 2001
  • Published electronically: February 12, 2002
  • © Copyright 2002 by the authors
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2327-2339
  • MSC (2000): Primary 53C42; Secondary 49Q20
  • DOI: https://doi.org/10.1090/S0002-9947-02-02983-5
  • MathSciNet review: 1885654