Stability, energy functional, and Kähler-Einstein metrics

Communications in Analysis and Geometry

Volumn 11, Issue 3, 2003, Pages 565-597

  Phong, D H ^a   Sturm, Jacob ^b  

^a Howard Hughes Medical Institute   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942533318     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.2003.v11.n3.a6     Document Type: Article

References (28)

1. [BM] Bando, S. and T. Mabuchi, "Uniqueness of Einstein-Kähler metrics modulo connected group actions", in Algebraic Geometry, Sendai 1985, Adv. Stud, in Pure Math. 10 (1987) 11-40, Kinokuniya, Tokyo and North-Holland, Amsterdam.
2. [C1] Chen, X., "On the lower bound of the Mabuchi energy and its application", Int. Math. Res. Notices 12 (2000) 607-623.
3. [C2] Chen, X., "The space of Kähler metrics", J. Differential Geom. 56 (2000) 189-234.
4. [De] Deligne, P., "Le determinant de la cohomologie", Contemporary Math. 67 (1987) 93-177.
5. [DT] Ding, W. and G. Tian, "Kähler-Einstein metrics and the generalized Futaki invariants", Inventiones Math. 110 (1992) 315-335.
6. [D1] Donaldson, S., "Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles", Proc. London Math. Soc. 50 (1985) 1-26.
7. [D2] Donaldson, S., "Scalar curvature and projective imbeddings I", 2001 Preprint.
8. [D3] Donaldson, S., "Infinite determinants, stable bundles, and curvature", Duke Math. J. 54 (1987) 231-247.
9. [F] Futaki, A., "On a character of the automorphism group of a compact complex manifold", Inventiones Math. 87 (1987) 655-660.
10. [KN] Kempf, G. and L. Ness, "The length of vectors in representation spaces", Algebraic Geometry (Proc. 1978 Summer Meeting, Copenhagen), Lecture Notes in Math. 732 (1979) 233-243, Springer-Verlag.
11. [Lu1] Lu, Z., "On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch", Amer. J. Math. 122 (2000) 235-273.
12. [Lu2] Lu, Z., "K-energy and K-stability for hypersurfaces", math.DG/0108009
13. [Luo] Luo, H., "Geometric criterion for Gieseker-Mumford stability of polarized manifolds", J. Diff. Geom. 49 (1998) 577-599.
14. [M] Mabuchi, T., "K-energy maps integrating Futaki invariants", Tohoku Math. J. 38 (1986) 245-257.
15. [Mu] Mumford, D., "Stability of projective varieties", L'Enseignement Mathematique, 23 (1977) 39-110.
16. [P] Paul, S. "Geometric analysis of Chow Mumford stability", Princeton Ph.D. Thesis (2000).
17. [SY] Siu, Y.T. and S.T. Yau, "Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay", Ann. of Math. 105 (1977) 225-264.
18. [T1] Tian, G., "The K-energy on hypersurfaces and stability", Comm. Anal. Geometry 2 (1994) 239-265.
19. [T2] Tian, G., "Kähler-Einstein metrics with positive scalar curvature", Inventiones Math. 130 (1997) 1-37.
20. [T3] Tian, G., "Canonical Metrics in Kähler Geometry", Birkhäuser, Basel, 2000.
21. [T4] Tian, G., "Bott-Chern forms and geometric stability", Discrete Contin. Dynam. Systems 6 (2000) 211-220.
22. [UY] Uhlenbeck, K. and S.T. Yau, "On the existence of Hermitian Yang-Mills connections on stable vector bundles", Commun. Pure Appl. Math. 39 (1986) 257-293.
23. [W] Wang, X., "Balance point and stability of vector bundle over projective manifolds", Brandeis 2001 preprint.
24. [Y1] Yau, S.T., "On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampere equation I", Comm. Pure Appl. Math. 31 (1978) 339-411.
25. [Y2] Yau, S.T., "Open Problems in Geometry", Proc. Symposia Pure Math. 54 (1993) 1-28.
26. [Y3] Yau, S.T., "Review of Kähler-Einstein metrics in Algebraic Geometry", Israel Math. Conf. Proceedings 9 (1996) 433-443.
27. [Y4] Yau, S.T., "Nonlinear analysis in geometry", Enseign. Math. 33 (1987) 109-158.
28. [Z] Zhang, S., "Heights and reductions of semi-stable varieties", Compositio Math. 104 (1996) 77-105.