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Convex affine surfaces with constant affine mean curvature

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Global Differential Geometry and Global Analysis

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References

  1. Blaschke, W.: Vorlesungen über Differentialgeometrie II, Affine Differentialgeometrie. Berlin J. Springer 1923

    Google Scholar 

  2. Calabi, E.: The improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens. Mich. Math. J., 5(1958), 105–126

    Article  MathSciNet  MATH  Google Scholar 

  3. Calabi, E.: Hypersurfaces with maximal affinely invariant area. Amer. Jour. of Math., 104(1982), 91–126

    Article  MathSciNet  MATH  Google Scholar 

  4. Calabi, E.: Convex affine-maximal surfaces. Results in Math., vol. 13(1988), 199–223

    Article  MathSciNet  MATH  Google Scholar 

  5. Cheng, S.Y., Yau, S.T.: Differential equations on Riemannian manifolds and their geometric applications. Comm. on Pure and Applied Math., 28(1975), 333–354

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheng, S.Y., Yau, S.T., Complete affine hypersurfaces, Part I. The completeness of Affine Metrics. Comm. on Pure and Applied Math., 39(1986), 839–866

    Article  MathSciNet  MATH  Google Scholar 

  7. Chern, S.S., Affine minimal hypersurfaces, Minimal Submanifolds and Geodesic., Kagai Publ., Ltd. Tokyo 1978, 17–30

    Google Scholar 

  8. Jörgens, K.: Über die Lösungen der Differentialgleichung rt-s2. Math. Ann., 127(1954), 180–184

    Article  Google Scholar 

  9. Kurose, T.: Two results in the affine hypersurface theory. J. Math. Soc. Japan, vol. 41, 3(1989), 539–548

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, A.M.: Affine maximal surfaces and harmonic functions. Lec. Notes, n. 1369(1986–87), 142–151

    Google Scholar 

  11. Li, A.M.: Some theorems in affine differential geometry. Acta Math. Sinica. To appear

    Google Scholar 

  12. Li, A.M., Penn, G.: Uniquess theorems in affine differential geometry, Part II. Results in Math., vol. 13(1988), 308–317

    Article  MathSciNet  MATH  Google Scholar 

  13. Martínez, A., Milán, F.: On the affine Bernstein Problem. Geom. Dedicata 37, No. 3, 295–302(1991)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pogorelov, A. V.: On the improper affine hyperspheres. Geometriae Dedicata, 1(1972), 33–46.

    Article  MathSciNet  MATH  Google Scholar 

  15. Simon, U.: Affine differential geometry. Proceedings Conf. Math. Reasearch Institute at Oberwolfach, Nov. 2–8, 1986

    Google Scholar 

  16. Simon, U.: Hypersurfaces in equiaffine differential geometry and eigenvalue problems. Proceedings Conf. Diff. Geom. Nové Mesto(CSSR) 1983; Part I, 127–136(1984)

    Google Scholar 

  17. Simon, U.: Hypersurfaces in equiaffine differential geometry, Geometriae Dedicata, 17(1984), 157–168

    Article  MathSciNet  MATH  Google Scholar 

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Dirk Ferus Ulrich Pinkall Udo Simon Berd Wegner

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© 1991 Springer-Verlag

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Martínez, A., Milán, F. (1991). Convex affine surfaces with constant affine mean curvature. In: Ferus, D., Pinkall, U., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 1481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083637

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  • DOI: https://doi.org/10.1007/BFb0083637

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54728-0

  • Online ISBN: 978-3-540-46445-7

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