C1,1 regularity for degenerate complex Monge–Ampère equations and geodesic rays

By Jianchun Chu, Valentino Tosatti, B. Weinkove. 2017

60 citations recorded by the source corpus.

ABSTRACT We prove a C1,1 estimate for solutions of complex Monge–Ampère equations on compact Kähler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This strengthens previous estimates of Phong–Sturm. As applications we deduce the local C1,1 regularity of geodesic rays in the space of Kähler metrics associated to a test configuration, as well as the local C1,1 regularity of quasi-psh envelopes in nef and big classes away from the non-Kähler locus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e4a82f7774921a326b66f9376bb5b2960e9ce4a0

Citations in the corpus

• Geodesic rays and stability in the cscK problem (2020, unknown): “It is known that Φ is C1,1 on X×C∗ ([22, 46]).”