Isoperimetric Regions in Rotationally Symmetric Convex Bodies

Indiana University Mathematics Journal

Volumn 52, Issue 5, 2003, Pages 1201-1214

  Rosales, César ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Constant mean curvature hypersurfaces; Isoperimetric problem; Isoperimetric regions; Stability

Indexed keywords

EID: 0242595954     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2003.52.2320     Document Type: Article

References (17)

1. J.L. BARBOSA and P. BÉRARD, Eigenvalue and "twisted" eigenvalue problems, applications to CMC surfaces, J. Math. Pures Appl. 79 (2000), 427-450.
2. J.L. BARBOSA and M. DO CARMO, Stability of hypersurfaces with constant mean curvature, Math. Z. 185 (1984), 339-353.
3. H. BRÉZIS and D. KINDERLEHRER, The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. J. 23 (1974), 831-844.
4. I. CHAVEL, Isoperimetric Inequalities. Differential Geometric and Analytic Perspectives, Cambridge Tracts in Mathematics Volume 145, Cambridge University Press, Cambridge, 2001.
5. _, Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984.
6. E. GIUSTI, Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, Volume 80, Birkhäuser Verlag, Basel-Boston, 1984.
7. E. GONZALEZ, U. MASSARI, and I. TAMANINI, On the regularity of sets minimizing perimeter with a volume constraint, Indiana Univ. Math. J. 32 (1983), 25-37.
8. _, Minimal boundaries enclosing a given volume, Manuscripta Math. 34 (1981), 381-395.
9. M. GRÜTER, Boundary regularity for solutions of a partitioning problem, Arch. Rat. Mech. Anal. 97 (1987), 261-270.
10. M. HUTCHINGS, F. MORGAN, M. RITORÉ, and A. ROS, Proof of the double bubble conjecture, Ann. Math. 155 (2002), 459-489.
11. P. MANI-LEVITSKA, Characterizations of convex sets, Handbook of Convex Geometry, Volume A, Elsevier Science Publishers, Amsterdam, 1993, pp. 19-41.
12. RENATO H.L. PEDROSA and MANUEL RITORÉ, Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems, Indiana Univ. Math. J. 48 (1999), 1357-1394.
13. A. ROS and E. VERGASTA, Stability for hypersurfaces of constant mean curvature with free boundary, Geom. Dedicata 56 (1995), 19-33.
14. N. ROUCHE and J. MAWHIN, Équations Différentielles Ordinaires. Tome 1: Théorie Générale, Masson et Cie, Éditeurs, Paris, 1973.
15. P. STERNBERG and K. ZUMBRUN, On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint, Comm. Anal. Geom 7 (1999), 199-220.
16. E. STREDULINSKY and WILLIAM. P. ZIEMER, Area minimizing sets subject to a volume constraint in a convex set, J. Geom. Anal. 7 (1997), 653-677.
17. G. TALENTI, The standard isoperimetric theorem, Handbook of Convex Geometry, Volume A, Elsevier Science Publishers, Amsterdam, 1993, pp. 73-123.