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
DOI:
https://doi.org/10.1090/S0002-9939-1987-0870791-8
MathSciNet review:
870791
Full-text PDF Free Access
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 ${{\mathbf {R}}^n}$.
-
E. De Giorgi, F. Colombini, and L. C. Piccinini, Frontiere orientate di misura minima e questioni collegate, Editrice Tecnico Scientifica, Pisa, 1972.
- Enrico Giusti, Minimal surfaces and functions of bounded variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel, 1984. MR 775682
- Umberto Massari, Esistenza e regolarità delle ipersuperfice di curvatura media assegnata in $R^{n}$, Arch. Rational Mech. Anal. 55 (1974), 357–382 (Italian). MR 355766, DOI https://doi.org/10.1007/BF00250439
- Umberto Massari, Frontiere orientate di curvatura media assegnata in$L^{p}$, Rend. Sem. Mat. Univ. Padova 53 (1975), 37–52 (Italian). MR 417905
- 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
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 49F22, 49F20
Retrieve articles in all journals with MSC: 49F22, 49F20
Additional Information
Article copyright:
© Copyright 1987
American Mathematical Society
