On the Lower Bound of the Mabuchi Energy and Its Application

International Mathematics Research Notices

Volumn 2000, Issue 12, 2000, Pages

  Chen, Xiuxiong ^a  

^a PRINCETON UNIVERSITY   (United States)

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EID: 0041759050     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. S. Bando and T. Mabuchi, "Uniqueness of Einstein Kähler metrics modulo connected group actions" in Algebraic Geometry (Sendai, 1985), Adv. Stud. Pure Math. 10, North-Holland, Amsterdam, 1987, 11-40.
2. E. D. Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), 1-44.
3. L. Caffarelli, J. Kohn, L. Nirenberg, and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations, II: Complex Monge-Ampère, and uniformaly elliptic, equations, Comm. Pure Appl. Math. 38 (1985), 209-252.
4. L. Caffarelli, L. Nirenberg, and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations, I: Monge-Ampère equation, Comm. Pure Appl. Math. 37 (1984), 369-402.
5. E. Calabi, "Extremal Kähler metrics" in Seminar on Differential Geometry, Ann. of Math. Stud. 102, Princeton Univ. Press, Princeton, 1982, 259-290.
6. E. Calabi and X. Chen, Space of Kähler metrics and Calabi flow, preprint, 1999.
7. X. Chen, Space of Kähler metrics, to appear in J. Differential Geom.
8. X. Chen and S. K. Donaldson, private communication, 1999.
9. W. Ding and G. Tian, "The generalized Moser-Trudinger inequality" in Proceedings of NanKai International Conference on Nonlinear Analysis and Microlocal Analysis, World Scientific, Singapore, 1992, 57-70.
10. S. K. Donaldson, Moment maps and diffeomorphisms, Asian J. Math. 3 (1999), 1-15.
11. _, "Symmetric spaces, Kähler geometry and Hamiltonian dynamics" in Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc., Providence, 1999, 13-33.
12. L. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. 35 (1982), 333-363.
13. S. Kołodziej, The complex Monge-Ampère equation, Acta Math. 180 (1998), 69-117.
14. N. V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Math. Appl. (Soviet Ser.) 7, Reidel, Dordrecht, 1987.
15. _, On the general notion of fully nonlinear second-order elliptic equations, Trans. Amer. Math. Soc. 347 (1995), 857-895.
16. P. Lelong, "Discontinuité et annulation de l'opérateur de Monge-Ampère complexe" in P. Lelong-P. Dolbeault-H. Skoda Analysis Seminar 1981/1983, Lecture Notes in Math. 1028, Springer, Berlin, 1983, 219-224.
17. L. Lempert, Solving the degenerate complex Monge-Ampère equation with one concentrated singularity, Math. Ann. 263 (1983), 515-532.
18. T. Mabuchi, Some symplectic geometry on compact Kähler manifolds, I, Osaka J. Math. 24 (1987), 227-252.
19. S. Semmes, Complex Monge-Ampère and symplectic manifolds, Amer. J. Math. 114 (1992), 495-550.
20. G. Tian, The K-energy on hypersurfaces and stability, Comm. Anal. Geom. 2 (1994), 239-265.
21. _, Kähler-Einstein metrics with positive scalar curvature, Invent. Math. 130 (1997), 1-37.
22. _, Some aspects of Kähler geometry, lecture notes taken by Meike Akeveld, 1997.
23. N. Trudinger, On the Dirichlet problem for Hessian equations, Acta Math. 175 (1995), 151-164.
24. S. T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, I, Comm. Pure Appl. Math. 31 (1978), 339-411.