Journal of Differential Geometry

Volume estimates for Kähler-Einstein metrics: The three-dimensional case

X.-X. Chen and S. K. Donaldson

Full-text: Open access

Abstract

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).

Article information

Source
J. Differential Geom., Volume 93, Number 2 (2013), 175-189.

Dates
First available in Project Euclid: 25 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1361800864

Digital Object Identifier
doi:10.4310/jdg/1361800864

Mathematical Reviews number (MathSciNet)
MR3024304

Zentralblatt MATH identifier
1279.32020

Citation

Chen, X.-X.; Donaldson, S. K. Volume estimates for Kähler-Einstein metrics: The three-dimensional case. J. Differential Geom. 93 (2013), no. 2, 175--189. doi:10.4310/jdg/1361800864. https://projecteuclid.org/euclid.jdg/1361800864


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