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February 2013 Volume estimates for Kähler-Einstein metrics: The three-dimensional case
X.-X. Chen, S. K. Donaldson
J. Differential Geom. 93(2): 175-189 (February 2013). DOI: 10.4310/jdg/1361800864


We obtain an estimate for the volumes of neighborhoods of sets of large curvature in three-dimensional Kähler-Einstein manifolds. The key technical step is to prove that a version of monotonicity for $L^2$ energy holds as long as the underlying region does not “carry homology” (in the sense that the normalized energy in a ball controls the normalized energy in an interior ball).


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X.-X. Chen. S. K. Donaldson. "Volume estimates for Kähler-Einstein metrics: The three-dimensional case." J. Differential Geom. 93 (2) 175 - 189, February 2013.


Published: February 2013
First available in Project Euclid: 25 February 2013

zbMATH: 1279.32020
MathSciNet: MR3024304
Digital Object Identifier: 10.4310/jdg/1361800864

Rights: Copyright © 2013 Lehigh University

Vol.93 • No. 2 • February 2013
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