The minimum sets and free boundaries of strictly plurisubharmonic functions
Complex Variables
2017-06-20 v1 Analysis of PDEs
Abstract
We study the minimum sets of plurisubharmonic functions with strictly positive Monge-Amp\`ere densities. We investigate the relationship between their Hausdorff dimension and the regularity of the function. Under suitable assumptions we prove that the minimum set cannot contain analytic subvarieties of large dimension. In the planar case we analyze the influence on the regularity of the right hand side and consider the corresponding free boundary problem with irregular data. We provide sharp examples for the Hausdorff dimension of the minimum set and the related free boundary. We also draw several analogues with the corresponding real results.
Keywords
Cite
@article{arxiv.1604.02826,
title = {The minimum sets and free boundaries of strictly plurisubharmonic functions},
author = {Slawomir Dinew and Zywomir Dinew},
journal= {arXiv preprint arXiv:1604.02826},
year = {2017}
}
Comments
16 pages