Monge-Ampere measures on pluripolar sets

Per Ahag; Urban Cegrell; Rafal Czyz; Pham Hoang Hiep

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arXiv · 0706.0169

Monge-Ampere measures on pluripolar sets

Per Ahag·Urban Cegrell·Rafal Czyz·Pham Hoang Hiep

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Abstract

In this article we solve the complex Monge-Ampere equation for measures with large singular part. This result generalizes classical results by Demailly, Lelong and Lempert a.o., who considered singular parts carried on discrete sets. By using our result we obtain a generalization of Kolodziej's subsolution theorem. More precisely, we prove that if a non-negative Borel measure is dominated by a complex Monge-Ampere measure, then it is a complex Monge-Ampere measure.

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Per Ahag, Urban Cegrell, Rafal Czyz, Pham Hoang Hiep. 2008-08-19. Monge-Ampere measures on pluripolar sets. https://arxiv.org/abs/0706.0169

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