Jianchun Chu, Valentino Tosatti, Ben Weinkove
Published 2017-07-12Version 1
We prove a $C^{1,1}$ estimate for solutions of complex Monge-Amp\`ere equations on compact K\"ahler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This strengthens previous estimates of Phong-Sturm. As applications we deduce the local $C^{1,1}$ regularity of geodesic rays in the space of K\"ahler metrics associated to a test configuration, as well as the local $C^{1,1}$ regularity of quasi-psh envelopes in nef and big classes away from the non-K\"ahler locus.
On the $C^{1,1}$ regularity of geodesics in the space of Kähler metrics
Envelope Approach to Degenerate Complex Monge-Ampère Equations on compact Kähler manifold
On the regularity of conical Calabi-Yau potentials
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