Author:
Kołodziej Sławomir,Nguyen Ngoc Cuong
Abstract
AbstractWe prove the existence of a continuous quasi-plurisubharmonic solution to the Monge–Ampère equation on a compact Hermitian manifold for a very general measure on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh–Nguyen–Sibony. As a consequence, we give a characterization of measures admitting Hölder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh–Nguyen.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference45 articles.
1. Bedford, E., Taylor, B.A.: A new capacity for plurisubharmonic functions. Acta Math. 149, 1–40 (1982)
2. Benelkourchi, S., Jennane, B., Zeriahi, A.: Polya’s inequalities, global uniform integrability and the size of plurisubharmonic lemniscates. Ark. Mat. 43, 85–112 (2005)
3. Caffarelli, L., Kohn, J., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex Monge–Ampère, and uniformly elliptic, equations. Commun. Pure Appl. Math. 38(2), 209–252 (1985)
4. Cegrell, U.: Pluricomplex energy. Acta Math. 180(2), 187–217 (1998)
5. Cherrier, P.: Équations de Monge–Ampère sur les variétés Hermitiennes compactes. Bull. Sci. Math. 111(2), 343–385 (1987)
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