On the existence of convex hypersurfaces with prescribed mean curvature

Kaising Tso

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)

  • Volume: 16, Issue: 2, page 225-243
  • ISSN: 0391-173X

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Tso, Kaising. "On the existence of convex hypersurfaces with prescribed mean curvature." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.2 (1989): 225-243. <http://eudml.org/doc/84052>.

@article{Tso1989,
author = {Tso, Kaising},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {mean curvature; Euler-Lagrange equation; convex hypersurface; negative gradient flow},
language = {eng},
number = {2},
pages = {225-243},
publisher = {Scuola normale superiore},
title = {On the existence of convex hypersurfaces with prescribed mean curvature},
url = {http://eudml.org/doc/84052},
volume = {16},
year = {1989},
}

TY - JOUR
AU - Tso, Kaising
TI - On the existence of convex hypersurfaces with prescribed mean curvature
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1989
PB - Scuola normale superiore
VL - 16
IS - 2
SP - 225
EP - 243
LA - eng
KW - mean curvature; Euler-Lagrange equation; convex hypersurface; negative gradient flow
UR - http://eudml.org/doc/84052
ER -

References

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  1. [BK] L. Bakelman, - B. Kantor, Existence of spherically homeomorphic hypersurfaces in Euclidean space with prescribed mean curvature, Geometry and Topology, Leningrad (1974), 3-10. 
  2. [CNS] L. Caffarelli - J. Nirenberg - J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations. IV: Starshaped compact Weingarten hypersurfaces, Current topics in partial differential equations, Ed. by Y. Ohya, K. Kasahara, N. Shimakura (1986), 1-26, Kinokunize Co., Tokyo. Zbl0672.35027MR1112140
  3. [F] H. Federer, Geometric Measure Theory, Springer-Verlag, Grundlehren 163, New York, 1969. Zbl0176.00801MR257325
  4. [H] R.S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom.17 (1982), 255-306. Zbl0504.53034MR664497
  5. [HU] G. Huisken, Flow by mean curvature of convex hypersurfaces into spheres, J. Differential Geom.20 (1984), 237-266. Zbl0556.53001MR772132
  6. [LSU] O. Ladyzenskaja - A. Solonnikov - N.N. Uralceva, Linear and quasilinear equations of parabolic type, Trans Amer. Math. Soc.23, Providence, 1968. Zbl0174.15403
  7. [P] A.V. Pogorelov, The Minkowski multidimensional problem, Nauka, Moscow, 1975 (in Russian); Engl. transl., John-Wiley and Sons, New York, 1978. Zbl0387.53023MR478079
  8. [T] A. Treibergs, Existence and convexity of hyperspheres of prescribed curvature, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (1985), 225-241. Zbl0599.53044MR829053
  9. [TW] A. Treibergs - S.W. Wei, Embedded hypersurfaces with prescribed mean curvature, J. Cl. Sci. (4) 18 (1983), 513-521. Zbl0529.53043MR723815
  10. [TS] K. Tso, Existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature, preprint 1989. MR1131436
  11. [Y] S.T. Yau, Problem section, Seminar on differential geometry, Ed. S. T. Yau, Ann. of Math. Stud., Princeton Univ. Press.102, 1982, 669-706. Zbl0479.53001MR645762

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