Monge-Ampere foliations for degenerate solutions
Complex Variables
2009-06-29 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.0906.4796,
title = {Monge-Ampere foliations for degenerate solutions},
author = {Morris Kalka and Giorgio Patrizio},
journal= {arXiv preprint arXiv:0906.4796},
year = {2009}
}