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Compactness theorems for critical metrics of the Weyl functional on compact Kähler surfaces

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Shun-Cheng Chang
Shun-Cheng Chang
Affiliation:
Department of Mathematics National Tsing Hua UniversityHsinchuTaiwan30043
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Abstract

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In this note, we propose an extension of the compactness property for Kähler-Einstein metrics to critical metrics of Weyl functional on compact Kähler surfaces.

MSC classification

Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C20: Global Riemannian geometry, including pinching
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 2 , April 1997 , pp. 217 - 228
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bando, S., Kasue, A. and Nakajima, H., ‘On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth’, Invent.Math. 97 (1989), 313–349.CrossRefGoogle Scholar
[2]Chang, S. C., ‘Critical Riemannian metrics’, Math. Z. (to appear).Google Scholar
[3]Derdziński, A., ‘Self-dual Kähler manifolds and Einstein manifolds of dimension four’, Compositio Math. 49 (1983), 405–433.Google Scholar
[4]Federer, H., Geometric measure theory (Springer, Berlin, 1969).Google Scholar
[5]Gao, L. Zhiyong, ‘Einstein metrics’, J. Differential Geom. 32 (1990), 155–183.CrossRefGoogle Scholar
[6]Gao, L. Zhiyong, ‘Convergence of Riemannian manifolds; Ricci pinching and L n/2-curvature pinching’, J. Differential Geom. 32 (1990), 349–381.CrossRefGoogle Scholar
[7]Gao, L. Zhiyong, ‘L n/2;-Curvature pinching’, J. Differential Geom. 32 (1990), 731–774.CrossRefGoogle Scholar
[8]Tian, G., ‘On Calabi's Conjecture for complex surfaces with positive first Chern class’, Invent.Math. 101 (1990), 101–172.CrossRefGoogle Scholar
[9]Tian, G., ‘Compactness theorems for Kähler-Einstein manifolds of dimension 3 and up’, J. Differential Geom. 35 (1992), 535–558.CrossRefGoogle Scholar