We prove a regularity result for Monge–Ampère equations degenerate along smooth divisor on Kähler manifolds in Donaldson’s spaces of ββ -weighted functions. We apply this result to study the curvature of Kähler metrics with conical singularities and give a geometric sufficient condition on the divisor for its boundedness
Arezzo, C., DELLA VEDOVA, A., La Nave, G. (2018). On the curvature of conic Kähler-Einstein metrics. THE JOURNAL OF GEOMETRIC ANALYSIS, 28(1), 265-283 [10.1007/s12220-017-9819-y].
On the curvature of conic Kähler-Einstein metrics
DELLA VEDOVA, ALBERTO;
2018
Abstract
We prove a regularity result for Monge–Ampère equations degenerate along smooth divisor on Kähler manifolds in Donaldson’s spaces of ββ -weighted functions. We apply this result to study the curvature of Kähler metrics with conical singularities and give a geometric sufficient condition on the divisor for its boundedness
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