Plongements radiaux S n R n + 1 à courbure de Gauss positive prescrite

Ph. Delanoë

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 4, page 635-649
  • ISSN: 0012-9593

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Delanoë, Ph.. "Plongements radiaux $S^n\hookrightarrow {R}^{n+1}$ à courbure de Gauss positive prescrite." Annales scientifiques de l'École Normale Supérieure 18.4 (1985): 635-649. <http://eudml.org/doc/82167>.

@article{Delanoë1985,
author = {Delanoë, Ph.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Monge-Ampere equation; a priori estimates; prescribed curvature; Gauss curvature problem; convex hypersurface},
language = {fre},
number = {4},
pages = {635-649},
publisher = {Elsevier},
title = {Plongements radiaux $S^n\hookrightarrow \{R\}^\{n+1\}$ à courbure de Gauss positive prescrite},
url = {http://eudml.org/doc/82167},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Delanoë, Ph.
TI - Plongements radiaux $S^n\hookrightarrow {R}^{n+1}$ à courbure de Gauss positive prescrite
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 4
SP - 635
EP - 649
LA - fre
KW - Monge-Ampere equation; a priori estimates; prescribed curvature; Gauss curvature problem; convex hypersurface
UR - http://eudml.org/doc/82167
ER -

References

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  2. [2] M. BERGER, P. GAUDUCHON et E. MAZET, Le Spectre d'une variété riemannienne (Lect. Notes Math., n° 194, Springer Verlag Berlin, Heidelberg, New York, 1971). Zbl0223.53034MR282313
  3. [3] S.-Y. CHENG et S.-T. YAU, On the regularity of the Solution of the n-Dimensional Minkowski Problem (Comm. Pure Appl. Math., vol. XXXIX, 1976, p. 495-516). Zbl0363.53030MR423267
  4. [4], [5], [6] Ph. DELANOË, Equations du type de Monge-Ampère sur les variétés riemanniennes compactes I, II, III, (J. Funct. Anal., vol. 40, n° 3, 1981, p. 358-386; vol. 41, n° 3, 1981, p. 341-353; vol. 45, n° 3, 1982, p. 403-430). Zbl0497.58026
  5. [7] Ph. DELANOË, Equations de Monge-Ampère invariantes sur les variétés riemanniennes Compactes (Ann. Inst. Henri Poincaré Anal. Non Linéaire, vol. 1, n° 3, 1984, p. 147-178). Zbl0555.58026MR778971
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  7. [9] J. LERAY et J. SCHAUDER, Topologie et équations fonctionnelles (Ann. Sci. Éc. Norm. Sup., vol. 51, 1934, p. 45-78). Zbl0009.07301JFM60.0322.02
  8. [10] C. B. MORREY, Multiple Integrals in the Calculus of Variations (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Band, 130, Springer-Verlag, Berlin, Heidelberg, New York, 1966). Zbl0142.38701MR202511
  9. [11] L. NIRENBERG, The Weyl and Minkowski Problems in Differential Geometry in the Large (Comm. Pure Appl. Math., vol. VI, 1953, p. 337-394). Zbl0051.12402MR58265
  10. [12] V. I. OLIKER, Hypersurfaces in ℝn + 1 with Prescribed Gaussian Curvature and Related Equations of Monge-Ampère Type, (Comm. P.D.E., vol. 9, n° 8, 1984, p. 807-838). Zbl0559.58031MR748368
  11. [13] A. V. POGORELOV, The Minkowski Multidimensional Problem (Winston-Wiley, 1978, New York, Toronto, London, Sydney). Zbl0387.53023MR478079
  12. [14] M. H. PROTTER et H. F. WEINBERGER, Maximum Principles in Differential Equations (Prentice-Hall, Inc., Englewood Cliffs, N.Y., 1967). Zbl0153.13602MR219861
  13. [15] A. E. TREIBERGS et S. WALTER WEI, Embedded Hyperspheres with prescribed Mean Curvature, (preprint M.S.R.I., 026-83, Berkeley, March 1983). Zbl0529.53043MR723815
  14. [16] B. M. VERESCHAGIN, Reconstruction d'une surface fermée convexe à partir de sa courbure de Gauss (Questions de Géométrie Globale, A. L. VERNER éd., Inst. Pédag. d'État de Léningrad, 1979, p. 7-12, en russe). Zbl0469.53050
  15. [17] YAU éd., Seminar on Differential Geometry (Ann. of Math. Studies, Study 102, Princeton University Press, Princeton N.J., 1982). Zbl0471.00020MR645728
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