The space of kähler metrics

Journal of Differential Geometry

Volumn 56, Issue 2, 2000, Pages 189-234

  Chen, Xiuxiong ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034287954     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1090347643     Document Type: Article

References (45)

1. T. Aubin, Equations du type de Monge-Ampère sur les varietes kãhleriennes compactes, C. R. Acad. Sci. Paris 283 (1976) 119-121.
2. T. Aubin, Nonlinear analysis on manifolds: Monge-Ampère equations, Spring, 1984.
3. S. Bando & T. Mabuchi, Uniquness of Einstein Kahler metrics modulo connected group actions, Algeb. Geom., Adv. Stud. Pure Math., 1987.
4. E. D. Bedford & T.A. Taylor, The Dirichlet problem for the complex Monge-Ampère operator, Invent. Math. 37 (1976) 1-44.
5. Guan Bo, The Dirichlet problem for complex Monge-Ampère equations and regu-larity of the plui-complex green function, Comm. Anal. Geom. 6 (1998) 687-703.
6. J. P. Bourguignon, Invariants integraux fonctionnels pour des equations aux de-rivees partielles d’origine geometrique, Lecture Notes in Math. 1209 (1985) 100-108.
7. J. P. Bourguignon, Metriques d’Einstein-Kahler sur les varietes de Favo: obstructions et existence, astérisque, Seminaire Bourbaki, 1996/1997(245), 1997.
8. D. Burns & P. de Bartolomeis, Stability of vector bundles and extremal metrics, Invent. Math. 92 (1992) 403-407.
9. E. Calabi, Extremal Kahler metrics, Seminar on Differential Geom., Ann. of Math. Stud. 16 (1982) 259-290.
10. K. Grove, P. Petersen & J.-Y. Wu, Geometric finiteness theorems via controlled topology, Extremai Kãhler metrics. II, Differential geometry and Complex analysis, Springer, 1985, pp. 96-114.
11. X. X. Chen, Extremai Hermitian metrics in Riemann Surface—Research an-noucenment, Internat. Math. Res. Notices, (15) (1998) 781-797.
12. X. X. Chen, Obstruction to the existence of extremai kähler metric in a surface with conical singularities, C.A.G. 8 (1), (2000).
13. R. R. Coifman & S. Semmes. Interpolation of Banach spaces, Perron process, and Yang-Mills, Amer. J. Math. 115 (1993) 243-278.
14. W. Ding & G. Tian, The generalized Moser-Trudinger inequality, Proc. NanKai Internat. Conf. Nonlinear Anal., 1993.
15. S. K. Donaldson, Remarks on gauge theory, complex geometry and 4-manifold topology, The Fields Medel Volume, (M.F. Atiyah and D. Iagolnitzer, eds.), World Scientific, 1997.
16. S. K. Donaldson, Symmetric spaces, Kãhler geometry and Hamiltonian dynamics, Private communication, 1996.
17. A. Fujiki, The moduli spaces and Kahler metrics of polarised algebraic varieties (Japanese), Vol. 42, Sugaku, 1992.
18. A. Fujiki, An obstruction to the existence of Einstein Kahler metrics, Invent. Math. 73 (1983) 437-443.
19. A. Fujiki, Kähler-Eistein metrics and integral invariants, Springer, 1988.
20. M. Klimek, Pluripotential theory, Oxford University Press, 1991.
21. S. Kolodziej, The complex Monge-Ampère equation, Acta Math. 180 (1998) 69117.
22. N. V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Number 7. D. Reidel Publishing Co., Dordrecht-Boston, 1987. Mathematics and its Applications (Soviet Series).
23. J.J. Kohn, L. Nirenberg, L. Caffarelli & J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equation, II. complex Monge-Ampère equation, Comm. Pure Appl. Math. 38 (1985) 209-252.
24. L. Nirenberg, L. Caffarelli & J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equation, I. Monge-Ampère equation, Comm. Pure Appl. Math. 37 (1984) 369-402.
25. C. Evans Lawrence, Classical solutions of fully nonlinear, convex, second order elliptic equations, Comm. Pure Appl. Math. 35 (1982) 333-363.
26. C. LeBrun, Polarized 4-manifolds, extremal Kähler Metrics, and Seiberg-Witten theory, Math. Res. Lett. 2 (1995) 653-662.
27. C. LeBrun & S. R. Simanca, Extremal Kähler metrics and complex deformation theory, Geom. Func. Anal. 4 (1994) 298-336.
28. P. Lelong, Discontinuite et annulation de l’operateur de Monge-Ampère complexe, in Seminarire, Lecture Notes in Math. Vol. 1028, Springer, 1983, pp 219-224.
29. L. Lempert, Solving the degenerate Monge-Ampère equation with one concentrated singularity, Math. Ann. 263 (1983) 515-532.
30. Marc Levine, A remark on extremal Kähler metrics, J. Differential Geom. 21 (1985) 73-77.
31. T. Mabuchi, Some Sympletic geometry on compact kahler manifolds. I, Osaka, J. Math. 24 (1987) 227-252.
32. 2 A Priori estimate for Degenerate Monge-Amèpre equations, Adv. Math. 86 (1997) 323-346.
33. Guan Pengfei, Regularity of a class of Quasilinear Degenerte elliptic equations, Adv. Math. 132 (1997) 24-45.
34. R. Rochberg, Interpolation of Banach spaces, differential geometry and differential equations, Pacific J. Math. 110 (1984) 355-376.
35. S. Semmes, Complex monge-ampère and symplectic manifolds, Amer. J. Math. 114 (1992) 495-550.
36. S. Semmes, The Homogenous complex Monge-ampère equation and the infinite di mensional versions of classic symmetric spaces, The Gelfand Math. Semminar, 1993-1995, pp. 225-242.
37. Z. Slodkowski, Complex Interpolation of normed and quasinormed spaces in sev-eral dimensions. I, Trans. Amer. Math. Soc. 308 (1988) 685-711.
38. 1(m) > 0, Invent. Math. 89 (1987) 225-246.
39. G. Tian, Kahler-Einstein metrics on algebraic manifolds, Lecture Notes in Math. Vol. 1646, 1996.
40. G. Tian, Kahler-Einstein metrics with positive scalar curvature, Invent. Math. 130 (1997) 1-39.
41. G. Tian, Some aspects of Kahler geometry, 1997. Lecture note taken by Meike Akeveld.
42. G. Tian, Private communication, 1998.
43. G. Tian & X. H. Zhu, Uniqueness of Kãhler-Ricci soliton, Preprint, 1998.
44. S. T. Yau, On the Ricci curvature of a compact Kãhler manifold and the complex Monge-Ampère equation, I*, Comm. Pure Appl. Math. 31 (1978) 339-441.
45. S. T. Yau, Open problems in differential geometry. Internat. Press, 1992.