Affiliation:
1. Institut de Mathematiques de Toulouse; UMR 5219, Universite de Toulouse; CNRS, UPS, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France
Abstract
Abstract
In this note, we investigate some regularity aspects for solutions of degenerate complex Monge–Ampère equations (DCMAE) on singular spaces. First, we study the Dirichlet problem for DCMAE on singular Stein spaces, showing a general continuity result. A consequence of our results is that Kähler–Einstein potentials are continuous at isolated singularities. Next, we establish the global continuity of solutions to DCMAE when the reference class belongs to the real Néron–Severi group. This yields in particular the continuity of Kähler–Einstein potentials on any irreducible Calabi–Yau variety.
Publisher
Oxford University Press (OUP)
Reference38 articles.
1. Algebraic approximation and the decomposition theorem for Kahler Calabi–Yau varieties;Bakker,2020
2. The Operator (dd$^c$)$^n$ on Complex Spaces;Bedford,1982
3. The Dirichlet problem for a complex Monge–Ampère equation;Bedford;Invent. Math.,1976
4. A new capacity for plurisubharmonic functions;Bedford;Acta Math.,1982
5. Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties;Berman;J. Reine Angew. Math.,2019
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献