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A K-energy characterization of extremal Kähler metrics
Author(s):
Santiago
R.
Simanca
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1531-1535.
MSC (1991):
Primary 58E11;
Secondary 53C55, 53C25
Posted:
August 5, 1999
MathSciNet review:
1664359
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Abstract:
We show that for any polarized compact Kähler manifold, the extremal Kähler metrics that represent the given cohomology class can be characterized as critical points of a suitably defined K-energy functional.
References:
- 1.
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- 2.
- E. Calabi, Extremal Kähler Metrics, in Seminar on Differential Geometry (ed. S.T. Yau) Princeton, 1982. MR 83i:53088
- 3.
- E. Calabi, Extremal Kähler Metrics II, in Differential Geometry and Complex Analysis (ed. I. Chavel and H.M. Farkas), Springer-Verlag, 1985. MR 86h:53067
- 4.
- W. Ding & G. Tian, Kähler-Einstein metrics and the generalized Futaki invariant, Invent. Math. 110 (1992) pp. 315-335. MR 93m:53039
- 5.
- A. Futaki, Kähler-Einstein Metrics and Integral Invariants, Lect. Notes in Math., 1314, Springer-Verlag. MR 90a:53053
- 6.
- C. LeBrun and S.R. Simanca, Extremal Kähler Metrics and Complex Deformation Theory, Geom. and Funct. Anal. 4 (1994), pp. 1-99. MR 95k:58041
- 7.
- T. Mabuchi, K-energy maps integrating Futaki invariants, Tohoku Math. Journal. 38 (1986), pp 575-593. MR 88b:53060
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Additional Information:
Santiago
R.
Simanca
Affiliation:
Department of Applied Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794-3600
Email:
santiago@ams.sunysb.edu
DOI:
10.1090/S0002-9939-99-05364-2
PII:
S 0002-9939(99)05364-2
Keywords:
Extremal K\"ahler metrics,
K-energy
Received by editor(s):
June 22, 1998
Posted:
August 5, 1999
Additional Notes:
The author was partially supported by the Gabriella and Paul Rosenbaum Foundation.
Communicated by:
Leslie Saper
Copyright of article:
Copyright
2000,
American Mathematical Society
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