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arXiv · 1009.4605

Maximal subextensions of plurisubharmonic functions

U. Cegrell·S. Kołodziej·A. Zeriahi
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Abstract

In this paper we are concerned with the problem of local and global subextensions of (quasi-)plurisubharmonic functions from a "regular" subdomain of a compact K\"ahler manifold. We prove that a precise bound on the complex Monge-Amp\`ere mass of the given function implies the existence of a subextension to a bigger regular subdomain or to the whole compact manifold. In some cases we show that the maximal subextension has a well defined complex Monge-Amp\`ere measure and obtain precise estimates on this measure. Finally we give an example of a plurisubharmonic function with a well defined Monge-Amp\`ere measure and the right bound on its Monge-Amp\`ere mass on the unit ball in $\C^n$ for which the maximal subextension to the complex projective space $\mb P_n$ does not have a globally well defined complex Monge-Amp\`ere measure.

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U. Cegrell, S. Kołodziej, A. Zeriahi. 2010-09-23. Maximal subextensions of plurisubharmonic functions. https://arxiv.org/abs/1009.4605

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