Estimates on Monge-Ampère operators derived from a local algebra inequality

Details Estimates on Monge-Ampère operators derived from a local algebra inequality Estimates on Monge-Ampère operators derived from a local algebra inequality

2007-09-21

arxiv.org/abs/0709.3524v2

Mathematics

Complex Variables

14 pages, dedicated to Christer Kiselman on the occasion of his retirement; the second version adds an Appendix by Ahmed Zeria

Scientific paper

The goal of this short note is to relate the integrability property of the exponential $e^{-2\phi}$ of a plurisubharmonic function $\phi$ with isolated or compactly supported singularities, to a priori bounds for the Monge-Amp\`ere mass of $(dd^c\phi)^n$. The inequality is valid locally or globally on an arbitrary open subset $\Omega$ in $\bC^n$. We show that $\int_\Omega(dd\phi)^n

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