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).
Citation
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. https://doi.org/10.4310/jdg/1361800864
Information