arXiv subjects
Publications and source records attributed to Guilherme Cerqueira-Gonçalves.
In this paper, we study the modulus of continuity of solutions to Dirichlet problems for complex Monge-Ampère equations with $L^p$ densities on Stein spaces with isolated singularities. In particular, we prove such solutions are Hölder continuous outside singular points if the boundary data is Hölder continuous.
In 1984 Gauduchon conjectured that one can find Gauduchon metrics with prescribed Ricci curvature on all compact complex manifolds. This conjecture was settled by Székelyhidi-Tosatti-Weinkove (TW17, TW19, STW17) by the study of the Monge-Ampère equation for $(n-1)$-plurisubharmonic functions with a gradient term. In this paper we study a singular version of this conjecture. We obtain a $C^{0}$-estimate for this problem, without gradient terms, in smoothable hermitian variaties by adapting a recent technique of Guedj-Lu. We also prove the smoothness of solutions on holomorphic Kähler families, generalizing TW17.