Estimates on Monge-Ampère operators derived from a local algebra inequality
| dc.creator | Demailly, Jean-Pierre | |
| dc.date | 2007-09-21 | |
| dc.date | 2007-11-27 | |
| dc.date.accessioned | 2026-07-07T08:44:45Z | |
| dc.date.available | 2026-07-07T08:44:45Z | |
| dc.description | The goal of this short note is to relate the integrability property of the exponential $e^{-2ϕ}$ of a plurisubharmonic function $ϕ$ with isolated or compactly supported singularities, to a priori bounds for the Monge-Ampère mass of $(dd^cϕ)^n$. The inequality is valid locally or globally on an arbitrary open subset $Ω$ in $\bC^n$. We show that $\int_Ω(ddϕ)^n<n^n$ implies $\int_Ke^{-2ϕ}<+\infty$ for every compact subset $K$ in $Ω$, while functions of the form $ϕ(z)=n\log|z-z_0|$, $z_0\inΩ$, appear as limit cases. The result is derived from an inequality of pure local algebra, which turns out a posteriori to be equivalent to it, proved by A.Corti in dimension $n=2$, and later extended by L.Ein, T.De Fernex and M.Mustaţǎ to arbitrary dimensions. | |
| dc.description | 14 pages, dedicated to Christer Kiselman on the occasion of his retirement; the second version adds an Appendix by Ahmed Zeriahi (Toulouse 3) | |
| dc.identifier | https://arxiv.org/abs/0709.3524 | |
| dc.identifier | http://arxiv.org/abs/0709.3524 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142772 | |
| dc.subject | Complex Variables | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32F07, 14B05, 14C17 | |
| dc.title | Estimates on Monge-Ampère operators derived from a local algebra inequality | |
| dc.type | text |