Existence and convexity for hyperspheres of prescribed mean curvature

Andrejs Treibergs

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1985)

  • Volume: 12, Issue: 2, page 225-241
  • ISSN: 0391-173X

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Treibergs, Andrejs. "Existence and convexity for hyperspheres of prescribed mean curvature." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 12.2 (1985): 225-241. <http://eudml.org/doc/83957>.

@article{Treibergs1985,
author = {Treibergs, Andrejs},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {prescribed mean curvature; convex hypersurfaces},
language = {eng},
number = {2},
pages = {225-241},
publisher = {Scuola normale superiore},
title = {Existence and convexity for hyperspheres of prescribed mean curvature},
url = {http://eudml.org/doc/83957},
volume = {12},
year = {1985},
}

TY - JOUR
AU - Treibergs, Andrejs
TI - Existence and convexity for hyperspheres of prescribed mean curvature
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1985
PB - Scuola normale superiore
VL - 12
IS - 2
SP - 225
EP - 241
LA - eng
KW - prescribed mean curvature; convex hypersurfaces
UR - http://eudml.org/doc/83957
ER -

References

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  3. [3] T. Aubin, Nonlinear Analysis on Manifolds, Monge-Ampere Equations, Springer-Verlag, New York, 1982. Zbl0512.53044MR681859
  4. [4] I. Bakelman - B. Kantor, Estimates for solutions of quasilinear elliptic equations connected with problems of geometry in the large, Mat. Sb., 91 (133) (1973), no. 3 = Math. USSR Sb., 20 (173) 3, pp. 348-363. Zbl0286.35034MR333441
  5. [5] I. Bakelman - B. Kantor, Existence of spherically homeomorphic hypersurfaces in Euclidean Space with prescribed mean curvature, Geometry and Topology, Leningrad, 1 (1974), pp. 3-10. MR423266
  6. [6] J.T. Chen - W. Huang, Convexity of capillary surfaces in outer space, to appear. Zbl0496.76005MR665156
  7. [7] W. Firey, Christoffel's problem for general convex bodies, Mathematika, 15 (1968), pp. 7-21. Zbl0162.54303MR230259
  8. [8] D. Gilbarg - N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1977. Zbl0361.35003MR473443
  9. [9] N. Korevaar, Convex solutions to nonlinear elliptic and parabolic boundary value problems, University of Wisconsin, Math. Res. Ctr. Tech. Rep. 2307 (1981), to appear in Indiana Univ. Math. J. Zbl0481.35024MR703287
  10. [10] V. Oliker, Hypersurfaces in Rn+1 with prescribed Gaussian curvature and related equations of Monge-Ampere type, preprint (1982). 
  11. [11] A. Pogorelov, Extrinsic Geometry of Convex Surfaces, AMS Translations of Mathematical Monographs35, Providence, 1973, pp. 435-442. Zbl0311.53067MR346714
  12. [12] J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc.London Ser. A264, pp. 413-496. Zbl0181.38003MR282058
  13. [13] A. Treibergs - S.W. Wei, Embedded hyperspheres with prescribed mean curvature, J. Diff. Geom., 18 (1983). Zbl0529.53043MR723815

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