Monge-Ampere foliations for degenerate solutions

Details Monge-Ampere foliations for degenerate solutions Monge-Ampere foliations for degenerate solutions

2009-06-25

arxiv.org/abs/0906.4796v1

Mathematics

Complex Variables

Scientific paper

We study the problem of the existence and the holomorphicity of the Monge-Amp\`ere foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Amp\`ere 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-Amp\`ere equation and we obtain a generalization the work of P.M. Wong on the classification of complete weighted circular domains.

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