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Volume estimates for kahler-einstein metrics: the three-dimensional case

X.-X. Chen Stony Brook University S.K. Donaldson Imperial College

Differential Geometry mathscidoc:1609.10296

Journal of Differential Geometry, 93, (2), 175-189, 2013
We obtain an estimate for the volumes of neighborhoods of sets of large curvature in three-dimensional K¨ahler-Einstein manifolds. The key technical step is to prove that a version of monotonicity for L2 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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@inproceedings{x.-x.2013volume,
  title={VOLUME ESTIMATES FOR KAHLER-EINSTEIN METRICS: THE THREE-DIMENSIONAL CASE},
  author={X.-X. Chen, and S.K. Donaldson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914073428297951958},
  booktitle={Journal of Differential Geometry},
  volume={93},
  number={2},
  pages={175-189},
  year={2013},
}
X.-X. Chen, and S.K. Donaldson. VOLUME ESTIMATES FOR KAHLER-EINSTEIN METRICS: THE THREE-DIMENSIONAL CASE. 2013. Vol. 93. In Journal of Differential Geometry. pp.175-189. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914073428297951958.
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