A priori estimates for weak solutions of complex Monge-Ampère equations
| dc.creator | Benelkourchi, S. | |
| dc.creator | Guedj, V. | |
| dc.creator | Zeriahi, A. | |
| dc.date | 2007-04-06 | |
| dc.date | 2008-02-22 | |
| dc.date.accessioned | 2026-07-07T09:22:09Z | |
| dc.date.available | 2026-07-07T09:22:09Z | |
| dc.description | Let $X$ be a compact Kähler manifold and $\om$ a smooth closed form of bidegree $(1,1)$ which is nonnegative and big. We study the classes ${\mathcal E}_χ(X,\om)$ of $\om$-plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight $χ$ has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class ${\mathcal E}_χ(X,\om)$. This is done by establishing a priori estimates on the capacity of sublevel sets of the solutions. Our result extends U.Cegrell's and S.Kolodziej's results and puts them into a unifying frame. It also gives a simple proof of S.T.Yau's celebrated a priori ${\mathcal C}^0$-estimate. | |
| dc.description | Corrected typos, added details to one proof | |
| dc.identifier | https://arxiv.org/abs/0704.0866 | |
| dc.identifier | http://arxiv.org/abs/0704.0866 | |
| dc.identifier | Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (5) Vol. VII (2008), 1-16 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155279 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 32W20, 32Q25, 32U05 | |
| dc.title | A priori estimates for weak solutions of complex Monge-Ampère equations | |
| dc.type | text |