Plongement isométrique de la sphère à courbure non négative dans R 3

C. Zuily

Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994)

  • page 1-9

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Zuily, C.. "Plongement isométrique de la sphère à courbure non négative dans $R^3$." Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994): 1-9. <http://eudml.org/doc/112093>.

@article{Zuily1993-1994,
author = {Zuily, C.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Weyl problem; nonnegative Gauss curvature; Monge-Ampère equation},
language = {fre},
pages = {1-9},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Plongement isométrique de la sphère à courbure non négative dans $R^3$},
url = {http://eudml.org/doc/112093},
year = {1993-1994},
}

TY - JOUR
AU - Zuily, C.
TI - Plongement isométrique de la sphère à courbure non négative dans $R^3$
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1993-1994
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 9
LA - fre
KW - Weyl problem; nonnegative Gauss curvature; Monge-Ampère equation
UR - http://eudml.org/doc/112093
ER -

References

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  1. [A] A.D. Alexandroff: Inirinsic geometry of convex surfaces, OGIZMoscow, 1948. 
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  3. [GL] P. Guan, Y.Y. Li: On Weyl problem with non negative Gauss curvature. (preprint). 
  4. [GW] R.E. Greene, H. Wu: C∞ convex functions and manifolds of positive curvature, Acta Math.137 (1976), 209-245. Zbl0372.53019
  5. [He1] E. Heinz: Neue a-priori-Abschätzungen..., Math. Zeitsch.74 (1960), 129-157. Zbl0096.36601MR116294
  6. [He2] E. Heinz: On Weyl's embedding problem, J. Math. Mech., 11 (1962), 421-454. Zbl0119.16604MR139127
  7. [Ho] J. Hong: Dirichlet problems for general Monge-Ampère equations, Math. Zeitsch.209 (1992), 289-308. Zbl0771.35020MR1147819
  8. [I] J. Iaia: Isometric embeddings of surfaces with non negative curvature in R3, Duke Math. Journ. 67 (2), (1992), 423-459. Zbl0777.53006MR1177314
  9. [N] L. Nirenberg: The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math.6 (1953), 337-394. Zbl0051.12402MR58265
  10. [P] A.V. Pogorelov: Extrinsic geometry of convex surfaces, Transl. Math. Monogr., Vol 35, Providence, RI: Am. Math. Soc.1973. Zbl0311.53067MR346714
  11. [S] R. Sacksteder: The rigidity of hypersurfaces, J. Math. Mech.11 (1962), 929-939. Zbl0108.34702MR144286
  12. [Sa] Sabitov: Regularity of convex surfaces with a metric that is regular in Hölder classes. Sib. Mat. J., 17 (1977), 681-687. Zbl0386.53041
  13. [W] H. Weyl: Über die Bestimmung einer geschlossen convex..., Vierteljahrschrift Naturforsch. Gesell, (Zürich), 61 (1916), 40-72. JFM46.1115.03

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