Minimal lagrangian diffeomorphisms and the monge-ampère equation

Journal of Differential Geometry

Volumn 46, Issue 2, 1997, Pages 335-373

  Wolfson, Jon G ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000391969     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214459935     Document Type: Article

References (23)

1. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math. 44 (1991) 375-417.
2. R. Bryant, Minimal lagrangian submanifolds of Kdhler-Einstein manifolds, Lecture Notes in Math. Vol. 1255, Springer, New York, 1987, 1-12.
3. 2, Amer. J. Math. 105 (1983) 975-1009.
4. L. Caffarelli, The regularity of mappings with a convex potential, J. Amer. Math. Soc. 5 (1992) 99-104.
5. L. Caffarelli, Boundary regularity of maps with convex potentials, Comm. Pure Appi. Math. 45 (1992) 1141-1151.
6. P. Dazard, Sur la géométrie des sous-fibrés et des feuilletages lagrangiens, Ann. Sci. École Norm. Sup.(4), 14 (1981) 465-480.
7. B. Dacorogna, &J. Moser, On a partial differential eguation involving the Jacobian determinant, Ann. Inst. H. Poincaré 7 (1990) 1-26.
8. P. Delanoë, Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator, Ann.Inst. H. Poincaré 8 (1991) 443-457.
9. Y. Eliashberg, Three lectures on symplectic topology, Proc. Conference on Differential Geom. Cala Gonne, 1988.
10. A. Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appi. Math. 41 (1988) 775-813.
11. M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307-347.
12. R. Harvey, &H. B. Lawson, Calibrated geometries, Acta. Math. 148 (1982) 47-157.
13. E. Hopf, A remark on linear elliptic differential eguations of second order, Proc. Amer. Math. Soc. 3 (1952) 791-793.
14. L. Hormander, The analysis of linear partial differential operators III, Springer, Berlin, 1985.
15. 1— structures, J. London Math. Soc. 45 (1992) 549-565.
16. Y.-I. Lee, Lagrangian minimal surfaces in Köhler-Einstein surfaces of negative scalar curvature, Preprint.
17. D. McDuff, The local behavior of holomorphic curves in almost complex 4-manifolds, J. Differential Geom. 34 (1991) 143-164.
18. T. Parker &J. Wolfson, Pseudo-holomorphic maps and bubble trees, J. Geom. Anal. 3 (1993) 63-98.
19. A. V. Pogorelov, Monge-Ampère eguations of elliptic type, P. Noordhoff, Groningen, 1964.
20. R. Schoen, The role of harmonic mappings in rigidity and deformation problems, Complex geometry, Proc. Osaka Internat, conference, Marcel Dekker, New York, 1993.
21. W. Wendland, Elliptic systems in the plane, Pitman, London, 1978.
22. J. Wolfson, unpublished, 1985.
23. J. Wolfson, Gromov’s compactness of pseudo-holomorphic curves and symplectic geometry, J. Differential Geom. 28 (1988) 383-405