Multiple convex hypersurfaces with prescribed mean curvature

Xi-Ping Zhu

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 2, page 175-191
  • ISSN: 0391-173X

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Zhu, Xi-Ping. "Multiple convex hypersurfaces with prescribed mean curvature." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.2 (1994): 175-191. <http://eudml.org/doc/84173>.

@article{Zhu1994,
author = {Zhu, Xi-Ping},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {prescribed mean curvature; mean curvature flow; convex hypersurfaces; mountain pass principle},
language = {eng},
number = {2},
pages = {175-191},
publisher = {Scuola normale superiore},
title = {Multiple convex hypersurfaces with prescribed mean curvature},
url = {http://eudml.org/doc/84173},
volume = {21},
year = {1994},
}

TY - JOUR
AU - Zhu, Xi-Ping
TI - Multiple convex hypersurfaces with prescribed mean curvature
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1994
PB - Scuola normale superiore
VL - 21
IS - 2
SP - 175
EP - 191
LA - eng
KW - prescribed mean curvature; mean curvature flow; convex hypersurfaces; mountain pass principle
UR - http://eudml.org/doc/84173
ER -

References

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  2. [2] L. Bakelman - B. Kantor, Existence of spherically homeomorphic hypersurfaces in Euclidean space with prescribed mean curvature, Geometry and Topology, Leningrad (1974), 3-10. 
  3. [3] L. Caffarelli - L. Nirenberg - J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalue of the Hessian, Acta Math.155 (1985), 261-301. Zbl0654.35031MR806416
  4. [4] L. Caffarelli - L. Nirenberg - J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations, IV: Starshaped compact Weingarten hypersurfaces, in Current topics in partial differential equations, Ed. by Y. Ohya - K. Kasahara- N. Shimakura, Kinokunize Co., Tokyo, 1986, 1-26. Zbl0672.35027MR1112140
  5. [5] K.S. Chou (TSO), Deforming a hypersurface by its Gauss-Kroneker curvature, Comm. Pure Appl. Math., 38 (1985), 867-882. Zbl0612.53005MR812353
  6. [6] K.S. Chou (TSO), On the existence of convex hypersurfaces with prescribed mean curvature, Ann. Scuola. Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), 225-243. Zbl0701.53078MR1041896
  7. [7] K.S. Chou (TSO), Convex hypersurfaces with prescribed Gauss-Kronecher curvature, J. Differential Geom., 34 (1991), 389-410. Zbl0723.53041MR1131436
  8. [8] N.V. Krylov, Nonlinear ellyptic and parabolic equations of second order, Reidel, Dordrecht, 1987. 
  9. [9] N.V. Krylov - M.V. Safonov, A certain property of solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk, 40 (1980), 161-175. English tranl., Math. USSR-Izv., 16 (1981), 151-164. Zbl0464.35035MR563790
  10. [10] M. Marcus - L. Lopes, Inequalities for symmetric functions and Hermitian matrices. Canad. J. Math., 8 (1956), 524-531. Zbl0079.02103MR84541
  11. [11] A. Treibergs - S.W. Wei, Embedded hypersurfaces with prescribed mean curvature, J. Diff. Geom. (4), 18 (1983), 513-521. Zbl0529.53043MR723815
  12. [12] J.I.E. Urbas, An expansion of convex hypersurfaces, J. Differential Geom., 33 (1991), 91-125. Zbl0746.53006MR1085136
  13. [13] S.T. Yau, Problem section, in Seminar on Differential Geometry, Ed. by S.T. Yau, Annals of Math. Studies, Princeton University Press, (1982), 669-706. Zbl0479.53001MR645762

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