Plongements radiaux S n ↪R n+1 à courbure de Gauss positive prescrite
Delanoë, Ph.
Annales scientifiques de l'École Normale Supérieure, Tome 18 (1985), p. 635-649 / Harvested from Numdam
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@article{ASENS_1985_4_18_4_635_0,
     author = {Delano\"e, Philippe},
     title = {Plongements radiaux $S^n\hookrightarrow {R}^{n+1}$ \`a courbure de Gauss positive prescrite},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {18},
     year = {1985},
     pages = {635-649},
     doi = {10.24033/asens.1498},
     mrnumber = {87j:53011},
     zbl = {0594.53039},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1985_4_18_4_635_0}
}

Delanoë, Ph. Plongements radiaux $S^n\hookrightarrow {R}^{n+1}$ à courbure de Gauss positive prescrite. Annales scientifiques de l'École Normale Supérieure, Tome 18 (1985) pp. 635-649. doi : 10.24033/asens.1498. http://gdmltest.u-ga.fr/item/ASENS_1985_4_18_4_635_0/

[1] I. Bakelman et B. Kantor, Existence of Spherically Homeomorphic Hypersurfaces in Euclidean Space with Prescribed Mean Curvature (Geometry and Topology, Léningrad, vol. 1, 1974, p. 3-10). | MR 423266

[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). | MR 282313 | Zbl 0223.53034

[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). | MR 423267 | Zbl 0363.53030

[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). | Zbl 0497.58026

[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). | Numdam | MR 778971 | Zbl 0555.58026

[8] Ph. Delanoë et A. Hirschowitz, About Nonlinear Elliptic Problems on Compact Manifolds (à paraître).

[9] J. Leray et J. Schauder, Topologie et équations fonctionnelles (Ann. Sci. Éc. Norm. Sup., vol. 51, 1934, p. 45-78). | JFM 60.0322.02 | Numdam | Zbl 0009.07301

[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). | MR 202511 | Zbl 0142.38701

[11] L. Nirenberg, The Weyl and Minkowski Problems in Differential Geometry in the Large (Comm. Pure Appl. Math., vol. VI, 1953, p. 337-394). | MR 58265 | Zbl 0051.12402

[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). | MR 748368 | Zbl 0559.58031

[13] A. V. Pogorelov, The Minkowski Multidimensional Problem (Winston-Wiley, 1978, New York, Toronto, London, Sydney). | MR 478079

[14] M. H. Protter et H. F. Weinberger, Maximum Principles in Differential Equations (Prentice-Hall, Inc., Englewood Cliffs, N.Y., 1967). | MR 219861 | Zbl 0153.13602

[15] A. E. Treibergs et S. Walter Wei, Embedded Hyperspheres with prescribed Mean Curvature, (preprint M.S.R.I., 026-83, Berkeley, March 1983). | MR 723815

[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). | Zbl 0469.53050

[17] Yau éd., Seminar on Differential Geometry (Ann. of Math. Studies, Study 102, Princeton University Press, Princeton N.J., 1982). | MR 645728 | Zbl 0471.00020

[18] L. Caffarelli, L. Nirenberg et J. Spruck, Nonlinear Second Order Elliptic Equations IV. Starshaped Compact Weingarten Hypersurfaces, (preprint 1985). | MR 1112140