Calabi Flow in Riemann Surfaces Revisited: A New Point of View

International Mathematics Research Notices

Volumn 2001, Issue 6, 2001, Pages

  Chen, X X ^a  

^a PRINCETON UNIVERSITY   (United States)

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EID: 0038525011     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. S. Bando and T. Mabuchi, "Uniqueness of Einstein Kähler metrics modulo connected group actions" in Algebraic Geometry (Sondai, Japan, 1985), Adv. Stud. Pure Math., North-Holland, Amsterdam, 1987,11-40.
2. E. Calabi, "Extremal Kähler metrics" in Seminar on Differential Geometry, Ann. of Math. Stud. 102, Princeton Univ. Press, Princeton, 1982, 259-290.
3. E. Calabi and X. X. Chen, Space of Kähler metrics and Calabi flow, submitted to J. Differential Geom.
4. S.-Y. A. Chang and J. Qing, The zeta functional determinants on manifolds with boundary, II: Extremal metrics and compactness of isospectral set, J. Funct. Anal. 147 (1997), 363-399.
5. S.-Y. A. Chang and P. C. Yang, Extremal metrics of zeta function determinants on 4-manifolds, Ann. of Math., 142 (1995), 171-212.
6. X. X. Chen, Extremal Hermitian metrics with curvature distortion in a Surface, Ph. D. dissertation, University of Pennsylvania, 1994.
7. _, Extremal Hermitian metrics on Riemannian surfaces, Internat. Math. Res. Notices 1998, 781-797.
8. _, Weak limits of Riemannian metrics in surfaces with integral curvature bound, Cale. Var. Partial Differential Equations 6 (1998), 189-226.
9. _, Extremal Hermitian metrics on Riemann surfaces, Calc. Var. Partial Differential Equations 8 (1999), 191-232.
10. _, Space of Kähler metrics, to appear in J. Differential Geom.
11. P. T. Chruściel, Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calabi) equation, Comm. Math. Phys. 137 (1991), 289-313.
12. S. K. Donaldson, "Symmetric spaces, Kahler geometry and Hamiltonian dynamics" in Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc., Providence, 1999.
13. Y. Y. Li, Harnack type inequality: The method of moving planes, Comm. Math. Phys. 200 (1999), 421-444.
14. T. Mabuchi, Some symplectic geometry on compact Kähler manifolds, I, Osaka J. Math. 24 (1987), 227-252.
15. B. Osgood, R. Phillips, and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), 148-211.
16. S. Semmes, Complex Monge-Ampère and sympletic manifolds, Amer. J. Math. 114 (1992), 495-550.
17. L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 (1983), 525-571.
18. M. S. Struwe, Curvature flows on surfaces, preprint, 2000.
19. G. Tian, Some aspects of Kähler geometry, lecture notes taken by Meike Akeveld, 1997.
20. X. W. Xu, On the existence of extremal metrics, Pacific J. Math. 174 (1996), 555-568.