Regularity of plurisubharmonic upper envelopes in big cohomology classes
| dc.creator | Berman, Robert | |
| dc.creator | Demailly, Jean-Pierre | |
| dc.date | 2009-05-08 | |
| dc.date.accessioned | 2026-07-07T13:13:03Z | |
| dc.date.available | 2026-07-07T13:13:03Z | |
| dc.description | The goal of this work is to prove the regularity of certain quasi-plurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of hermitian metrics with minimal singularities on a big line bundle over a compact complex manifold. We prove that the complex Hessian forms of these envelopes are locally bounded outside an analytic set of singularities. It is furthermore shown that a parametrized version of this result yields a priori inequalities for the solution of the Dirichlet problem for a degenerate Monge-Ampere operator; applications to geodesics in the space of Kahler metrics are discussed. A similar technique provides a logarithmic modulus of continuity for Tsuji's "supercanonical" metrics, which generalize a well-known construction of Narasimhan-Simha. | |
| dc.description | 27 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0905.1246 | |
| dc.identifier | http://arxiv.org/abs/0905.1246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229767 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.title | Regularity of plurisubharmonic upper envelopes in big cohomology classes | |
| dc.type | text |