Plurisubharmonic envelopes and supersolutions
Complex Variables
2017-03-17 v1 Analysis of PDEs
Differential Geometry
Abstract
We make a systematic study of (quasi-)plurisubharmonic envelopes on compact K\"ahler manifolds, as well as on domains of , by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Amp\`ere equation. We use these ideas to solve complex Monge-Amp\`ere equations by taking lower envelopes of super-solutions.
Cite
@article{arxiv.1703.05254,
title = {Plurisubharmonic envelopes and supersolutions},
author = {Vincent Guedj and Chinh H. Lu and Ahmed Zeriahi},
journal= {arXiv preprint arXiv:1703.05254},
year = {2017}
}