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Isometric embedding of the 2-sphere with non negative curvature in ℝ3

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References

  1. Alexandroff, A.D.: Intrinsic geometry of convex surfaces, OGIZ Moscow, 1948

    Google Scholar 

  2. Caffarelli, L., Nirenberg, L., Spruck, J.: The Dirichlet problem … I. Monge-Ampère equations, Comm. Pure Appl. Math.37, 369–402 (1984)

    MATH  MathSciNet  Google Scholar 

  3. Cheng, S.S., Yau, S.T.: On the regularity of the n-dimensionnal Minkowski problem, Comm. Pure Appl. Math.29, 495–516 (1976)

    MATH  MathSciNet  Google Scholar 

  4. Corona, C.M.: Monge-Ampère equations on convex regions of the plane, Comm. Part. Diff. Equ.16(1), 43–57 (1991)

    MATH  MathSciNet  Google Scholar 

  5. Darboux, G.: Théorie des surfaces, Vol. 3, Paris 1894

  6. Greene, R.E., Wu, H.:C ∞ convex functions and manifolds of positive curvature, Acta Math.137, 209–245 (1976)

    Article  MathSciNet  Google Scholar 

  7. Heinz, E.: Neue a-priori-Abschätzungen …, Math. Zeitsch.74, 129–157 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  8. Heinz, E.: On Weyl’s embedding problem, J. Math. Mech.,11, 421–454 (1962)

    MATH  MathSciNet  Google Scholar 

  9. Hong, J.: Dirichlet problems for general Monge-Ampére equations, Math. Zeitsch.209, 289–308 (1992)

    Article  MATH  Google Scholar 

  10. Iaia, J.: Isometric embedding of surfaces with non negative curvature in ℝ3, Duke Math. Journ.67(2), 423–459 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Nirenberg, L.: The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math.6, 337–394 (1953)

    MATH  MathSciNet  Google Scholar 

  12. Pogorelov, A.V.: Extrinsic geometry of convex surfaces, Transl. Math. Monogr., Vol35, Providence, RI: Am. Math. Soc. 1973

    MATH  Google Scholar 

  13. Sacksteder, R.: The rigidity of hypersurfaces, J. Math. Mech.11, 929–939 (1962)

    MATH  MathSciNet  Google Scholar 

  14. Schulze, F., Liang Yuan Liao: Regularity of solutions of two-dimensionnal Monge-Ampère equations, Trans. of A.M.S., Vol.307, no1, 271–277 (1988)

    Article  Google Scholar 

  15. Weyl, H.: Über die Bestimmung einer geschlossen convex …, Vierteljahrschrift Naturforsch. Gesell, (Zürich),61, 40–72 (1916)

    Google Scholar 

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Author notes

  1. J. Hong

    Present address: Institute of Mathematics, Fudan University Shanghaï, China

  2. C. Zuily

    Present address: Department de Mathématiques, Université de Paris-Sud, Mathématique Bât.425, F-91405, Orsay Cedex, France

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    1. J. Hong
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    2. C. Zuily
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    Hong, J., Zuily, C. Isometric embedding of the 2-sphere with non negative curvature in ℝ3 . Math Z 219, 323–334 (1995). https://doi.org/10.1007/BF02572368

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