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arXiv · 0906.4796

Monge-Ampere foliations for degenerate solutions

Morris Kalka·Giorgio Patrizio
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Abstract

We study the problem of the existence and the holomorphicity of the Monge-Ampère foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Ampère equation even at points of arbitrary degeneracy. We obtain good results for real analytic unbounded solutions. As a consequence we also provide a positive answer to a question of Burns on homogeneous polynomials whose logarithm satisfies the complex Monge-Ampère equation and we obtain a generalization the work of P.M. Wong on the classification of complete weighted circular domains.

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Morris Kalka, Giorgio Patrizio. 2009-06-25. Monge-Ampere foliations for degenerate solutions. https://arxiv.org/abs/0906.4796

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