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Volumn 356, Issue 11, 2004, Pages 4601-4622

Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

Author keywords

Hypersurfaces with constant mean curvature; Isoperimetric regions; Stability

Indexed keywords


EID: 7544223299     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03537-8     Document Type: Article
Times cited : (97)

References (28)
  • 1
    • 0000910006 scopus 로고
    • Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
    • MR 54:8420
    • [A] F. J. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. 4 (1976), no. 165, viii+199. MR 54:8420
    • (1976) Mem. Amer. Math. Soc. , vol.4 , Issue.165
    • Almgren Jr., F.J.1
  • 2
    • 0000142915 scopus 로고
    • Stability of hypersurfaces with constant mean curvature
    • MR 85k:58021c
    • [BdC] João Lucas Barbosa and Manfrede do Carmo, Stability of hypersurfaces with constant mean curvature, Math. Z. 185 (1984), no. 3, 339-353. MR 85k:58021c
    • (1984) Math. Z. , vol.185 , Issue.3 , pp. 339-353
    • Lucas Barbosa, J.1    Do Carmo, M.2
  • 3
    • 0000979948 scopus 로고
    • Inégalités isopérimétriques et applications
    • MR 84h:58147
    • [BM] Pierre Bérard and Daniel Meyer, Inégalités isopérimétriques et applications, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 3, 513-541. MR 84h:58147
    • (1982) Ann. Sci. École Norm. Sup. (4) , vol.15 , Issue.3 , pp. 513-541
    • Bérard, P.1    Meyer, D.2
  • 7
    • 0002246356 scopus 로고
    • On the regularity of boundaries of sets minimizing perimeter with a volume constraint
    • MR 84d:49043
    • [GMT] Eduardo Gonzalez, Umberto Massari, and Italo Tamanini, On the regularity of boundaries of sets minimizing perimeter with a volume constraint, Indiana Univ. Math. J. 32 (1983), no. 1, 25-37. MR 84d:49043
    • (1983) Indiana Univ. Math. J. , vol.32 , Issue.1 , pp. 25-37
    • Gonzalez, E.1    Massari, U.2    Tamanini, I.3
  • 8
    • 0003268230 scopus 로고    scopus 로고
    • Metric structures for Riemannian and non-Riemannian spaces
    • Birkhäuser Boston Inc., Boston, MA, based on the 1981 French original MR 85e:53051, with appendices by M. Katz, P. Pansu and S. Semmes. translated from the French by Sean Michael Bates. MR 2000d:53065
    • [Gr] Misha Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, vol. 152, Birkhäuser Boston Inc., Boston, MA, 1999, based on the 1981 French original MR 85e:53051, with appendices by M. Katz, P. Pansu and S. Semmes. translated from the French by Sean Michael Bates. MR 2000d:53065
    • (1999) Progress in Mathematics , vol.152
    • Gromov, M.1
  • 9
    • 0010215836 scopus 로고
    • Boundary regularity for solutions of a partitioning problem
    • MR 8Tk:49050
    • [G1] Michael Grüter, Boundary regularity for solutions of a partitioning problem, Arch. Rational Mech. Anal. 97 (1987), no. 3, 261-270. MR 8Tk:49050
    • (1987) Arch. Rational Mech. Anal. , vol.97 , Issue.3 , pp. 261-270
    • Grüter, M.1
  • 10
    • 1642627994 scopus 로고
    • Optimal regularity for codimension one minimal surfaces with a free boundary
    • MR 88m:49032
    • [G2] -, Optimal regularity for codimension one minimal surfaces with a free boundary, Manuscripta Math. 58 (1987), no. 3, 295-343. MR 88m:49032
    • (1987) Manuscripta Math. , vol.58 , Issue.3 , pp. 295-343
  • 11
    • 0010139417 scopus 로고
    • Allard type regularity results for varifolds with free boundaries
    • MR 89d:49048
    • [GJ] Michael Grüter and Jürgen Jost, Allard type regularity results for varifolds with free boundaries, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), no. 1, 129-169. MR 89d:49048
    • (1986) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.13 , Issue.1 , pp. 129-169
    • Grüter, M.1    Jost, J.2
  • 12
    • 0038900158 scopus 로고
    • Isoperimetric inequalities for convex cones
    • MR 90i:52021
    • [LP] Pierre-Louis Lions and Filomana Pacella, Isoperimetric inequalities for convex cones, Proc. Amer. Math. Soc. 109 (1990), no. 2, 477-485. MR 90i:52021
    • (1990) Proc. Amer. Math. Soc. , vol.109 , Issue.2 , pp. 477-485
    • Lions, P.-L.1    Pacella, F.2
  • 13
    • 0344928071 scopus 로고    scopus 로고
    • Regularity of isoperimetric hypersurfaces in Riemannian manifolds
    • to appear
    • [M1] Frank Morgan, Regularity of isoperimetric hypersurfaces in Riemannian manifolds. Trans. Amer. Math. Soc. (to appear).
    • Trans. Amer. Math. Soc.
    • Morgan, F.1
  • 14
    • 0003548677 scopus 로고    scopus 로고
    • A K Peters Ltd., Wellesley, MA, A beginner's guide. MR 98i:53001
    • [M2] -, Riemannian geometry, second ed., A K Peters Ltd., Wellesley, MA, 1998, A beginner's guide. MR 98i:53001
    • (1998) Riemannian Geometry, Second Ed.
  • 15
    • 0003418230 scopus 로고    scopus 로고
    • Academic Press Inc., San Diego, CA, A beginner's guide. MR 2001j:49001
    • [M3] -, Geometric measure theory, third ed., Academic Press Inc., San Diego, CA, 2000, A beginner's guide. MR 2001j:49001
    • (2000) Geometric Measure Theory, Third Ed.
  • 16
    • 0001192899 scopus 로고    scopus 로고
    • Some sharp isoperimetric theorems for Riemannian manifolds
    • MR 2002e:53043
    • [MJ] Frank Morgan and David L. Johnson. Some sharp isoperimetric theorems for Riemannian manifolds, Indiana Univ. Math. J. 49 (2000), no. 3, 1017-1041. MR 2002e:53043
    • (2000) Indiana Univ. Math. J. , vol.49 , Issue.3 , pp. 1017-1041
    • Morgan, F.1    Johnson, D.L.2
  • 17
    • 0036347610 scopus 로고    scopus 로고
    • Isoperimetric regions in cones
    • (electronic). MR 2003a:53089
    • [MR] Frank Morgan and Manuel Ritoré, Isoperimetric regions in cones. Trans. Amer. Math. Soc. 354 (2002), no. 6, 2327-2339 (electronic). MR 2003a:53089
    • (2002) Trans. Amer. Math. Soc. , vol.354 , Issue.6 , pp. 2327-2339
    • Morgan, F.1    Ritoré, M.2
  • 18
    • 0041906588 scopus 로고    scopus 로고
    • Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces
    • MR 2003a:53018
    • [R1] Manuel Ritoré, Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces, Comm. Anal. Geom. 9 (2001), no. 5, 1093-1138. MR 2003a:53018
    • (2001) Comm. Anal. Geom. , vol.9 , Issue.5 , pp. 1093-1138
    • Ritoré, M.1
  • 19
    • 0141793896 scopus 로고    scopus 로고
    • The isoperimetric problem in complete surfaces of nonnegative curvature
    • MR 2002f:53109
    • [R2] -, The isoperimetric problem in complete surfaces of nonnegative curvature, J. Geom. Anal. 11 (2001), no. 3, 509-517. MR 2002f:53109
    • (2001) J. Geom. Anal. , vol.11 , Issue.3 , pp. 509-517
  • 20
    • 0002440829 scopus 로고
    • Stability for hypersurfaces of constant mean curvature with free boundary
    • MR 96h:53013
    • [RV] Antonio Ros and Enaldo Vergasta, Stability for hypersurfaces of constant mean curvature with free boundary, Geom. Dedicata 56 (1995), no. 1, 19-33. MR 96h:53013
    • (1995) Geom. Dedicata , vol.56 , Issue.1 , pp. 19-33
    • Ros, A.1    Vergasta, E.2
  • 21
    • 0242595954 scopus 로고    scopus 로고
    • Isoperimetric regions in rotationally symmetric convex bodies
    • [R] César Rosales, Isoperimetric regions in rotationally symmetric convex bodies, Indiana U. Math. J. 52 (2003), no. 5, 1201-1214.
    • (2003) Indiana U. Math. J. , vol.52 , Issue.5 , pp. 1201-1214
    • Rosales, C.1
  • 22
    • 0001841087 scopus 로고
    • Lectures on geometric measure theory
    • Australian National University, Australian National University Centre for Mathematical Analysis, Canberra. MR 87a:49001
    • [S] Leon Sirnon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University Centre for Mathematical Analysis, Canberra, 1983. MR 87a:49001
    • (1983) Proceedings of the Centre for Mathematical Analysis , vol.3
    • Sirnon, L.1
  • 23
    • 0032221205 scopus 로고    scopus 로고
    • A poincaré inequality with applications to volume-constrained area-minimizing surfaces
    • MR 99g:58028
    • [SZ1] Peter Sternberg and Kevin Zumbrun, A Poincaré inequality with applications to volume-constrained area-minimizing surfaces, J. Reine Angew. Math. 503 (1998), 63-85. MR 99g:58028
    • (1998) J. Reine Angew. Math. , vol.503 , pp. 63-85
    • Sternberg, P.1    Zumbrun, K.2
  • 24
    • 0010033998 scopus 로고    scopus 로고
    • On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint
    • MR 2000d:49062
    • [SZ2] -, On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint, Comm. Anal. Geom. 7 (1999). no. 1, 199-220. MR 2000d:49062
    • (1999) Comm. Anal. Geom. , vol.7 , Issue.1 , pp. 199-220
  • 25
    • 0242672014 scopus 로고    scopus 로고
    • Area minimizing sets subject to a volume constraint in a convex set
    • MR 99k:49089
    • [StZ] Edward Stredulinsky and William P. Ziemer, Area minimizing sets subject to a volume constraint in a convex set, J. Geom. Anal. 7 (1997), no. 4, 653-677. MR 99k:49089
    • (1997) J. Geom. Anal. , vol.7 , Issue.4 , pp. 653-677
    • Stredulinsky, E.1    Ziemer, W.P.2
  • 26
    • 84974000887 scopus 로고
    • A note on the stability theorem of J. L. Barbosa and M. Do Carmo for closed surfaces of constant mean curvature
    • MR 92g:53010
    • [W] Henry C. Wente, A note on the stability theorem of J. L. Barbosa and M. Do Carmo for closed surfaces of constant mean curvature, Pacific J. Math. 147 (1991), no. 2, 375-379. MR 92g:53010
    • (1991) Pacific J. Math. , vol.147 , Issue.2 , pp. 375-379
    • Wente, H.C.1
  • 27
    • 0004227490 scopus 로고
    • Princeton University Press, Princeton, N. J. MR 19:309c
    • [Wh] Hassler Whitney, Geometric integration theory, Princeton University Press, Princeton, N. J., 1957. MR 19:309c
    • (1957) Geometric Integration Theory
    • Whitney, H.1
  • 28
    • 0004095766 scopus 로고
    • Graduate Texts in Mathematics, Springer-Verlag, New York. Sobolev spaces and functions of bounded variation. MR 91e:46046
    • [Z] William P. Ziemer, Weakly differentiate functions, Graduate Texts in Mathematics, vol. 120, Springer-Verlag, New York. 1989. Sobolev spaces and functions of bounded variation. MR 91e:46046
    • (1989) Weakly Differentiate Functions , vol.120
    • Ziemer, W.P.1


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