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.References
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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