Monge-Ampere foliations for degenerate solutions - Mathematics > Complex VariablesReport as inadecuate




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Abstract: We study the problem of the existence and the holomorphicity of theMonge-Amp\`ere foliation associated to a plurisubharmonic solutions of thecomplex homogeneous Monge-Amp\`ere equation even at points of arbitrarydegeneracy. We obtain good results for real analytic unbounded solutions. As aconsequence we also provide a positive answer to a question of Burns onhomogeneous polynomials whose logarithm satisfies the complex Monge-Amp\`ereequation and we obtain a generalization the work of P.M. Wong on theclassification of complete weighted circular domains.



Author: Morris Kalka, Giorgio Patrizio

Source: https://arxiv.org/







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