An Extension to a Theorem of Jörgens, Calabi, and Pogorelov

Communications on Pure and Applied Mathematics

Volumn 56, Issue 5, 2003, Pages 549-583

  Caffarelli, L ^a   Li, Yanyan ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037258897     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.10067     Document Type: Article

References (19)

1. Aubin, T. Équations de Monge-Ampère réelles. J. Funct. Anal. 41 (1981), no. 3, 354-377.
2. 2,p estimates for solutions of the Monge-Ampère equation. Ann. of Math. (2) 131 (1990), no. 1, 135-150.
3. Caffarelli, L. A. A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Ann. of Math. (2) 131 (1990), no. 1, 129-134.
4. Caffarelli, L. A. Topics in PDEs: The Monge-Ampère equation. Graduate course. Courant Institute, New York University, 1995.
5. Caffarelli, L. A.; Cabré, X. Fully nonlinear elliptic equations. American Mathematical Society Colloquium Publications, 43. American Mathematical Society, Providence, R.I., 1995.
6. Caffarelli, L.; Nirenberg, L.; Spruck, J. The Dirichlet problem for nonlinear second-order elliptic equations. I. Monge-Ampère equation. Comm. Pure Appl. Math. 37 (1984), no. 3, 369-402.
7. Calabi, E. Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens. Michigan Math. J. 5 (1958), 105-126.
8. j) = F(x, u). Comm. Pure Appl. Math. 30 (1977), no. 1, 41-68.
9. Cheng, S. Y.; Yau, S. T. Complete affine hypersurfaces. I. The completeness of affine metrics. Comm. Pure Appl. Math. 39 (1986), no. 6, 839-866.
10. Chou, K.-S.; Wang, X.-J. Entire solutions of the Monge-Ampère equation. Comm. Pure Appl. Math. 49 (1996), no. 5, 529-539.
11. n. Lecture Notes in Mathematics, 481. Springer, Berlin-New York, 1975.
12. Delanoë, P. Partial decay on simple manifolds. Ann. Global Anal. Geom. 10 (1992), no. 1, 3-61.
13. Ferrer, L.; Martínez, A.; Milán, F. An extension of a theorem by K. Jörgens and a maximum principle at infinity for parabolic affine spheres. Math. Z. 230 (1999), no. 3, 471-486.
14. Ferrer, L.; Martínez, A.; Milán, F. The space of parabolic affine spheres with fixed compact boundary. Monatsh. Math. 130 (2000), no. 1, 19-27.
15. Gilbarg, D.; Serrin, J. On isolated singularities of solutions of second order elliptic differential equations. J. Analyse Math. 4 (1955/56), 309-340.
16. Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order. Second edition. Grundlehren der Mathematischen Wissenschaften, 224. Springer, Berlin, 1983.
17. 2 = 1. Math. Ann. 127 (1954), 130-134.
18. Pogorelov, A. V. On the improper convex affine hyperspheres. Geometriae Dedicata 1 (1972), no. 1, 33.
19. Trudinger, N. S.; Wang, X.-J. The Bernstein problem for affine maximal hypersurfaces. Invent. Math. 140 (2000), no. 2, 399-422.