$C^{1,1}$ regularity for degenerate complex Monge-Amp\`ere equations and geodesic rays
Differential Geometry
2018-03-22 v2
Abstract
We prove a 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 regularity of geodesic rays in the space of K\"ahler metrics associated to a test configuration, as well as the local regularity of quasi-psh envelopes in nef and big classes away from the non-K\"ahler locus.
Cite
@article{arxiv.1707.03660,
title = {$C^{1,1}$ regularity for degenerate complex Monge-Amp\`ere equations and geodesic rays},
author = {Jianchun Chu and Valentino Tosatti and Ben Weinkove},
journal= {arXiv preprint arXiv:1707.03660},
year = {2018}
}
Comments
23 pages; v2: a minor correction