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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The mean curvature of a set of finite perimeter


Authors: Elisabetta Barozzi, Eduardo Gonzalez and Italo Tamanini
Journal: Proc. Amer. Math. Soc. 99 (1987), 313-316
MSC: Primary 49F22; Secondary 49F20
MathSciNet review: 870791
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that an arbitrary set of finite perimeter in $ {{\mathbf{R}}^n}$ minimizes some prescribed mean curvature functional given by an $ {L^1}$ function on $ {{\mathbf{R}}^n}$.


References [Enhancements On Off] (What's this?)

  • [1] E. De Giorgi, F. Colombini, and L. C. Piccinini, Frontiere orientate di misura minima e questioni collegate, Editrice Tecnico Scientifica, Pisa, 1972.
  • [2] Enrico Giusti, Minimal surfaces and functions of bounded variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel, 1984. MR 775682 (87a:58041)
  • [3] Umberto Massari, Esistenza e regolarità delle ipersuperfice di curvatura media assegnata in 𝑅ⁿ, Arch. Rational Mech. Anal. 55 (1974), 357–382 (Italian). MR 0355766 (50 #8240)
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  • [5] Umberto Massari and Mario Miranda, Minimal surfaces of codimension one, North-Holland Mathematics Studies, vol. 91, North-Holland Publishing Co., Amsterdam, 1984. Notas de Matemática [Mathematical Notes], 95. MR 795963 (87f:49058)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870791-8
PII: S 0002-9939(1987)0870791-8
Article copyright: © Copyright 1987 American Mathematical Society