English

The complex Monge-Amp\'{e}re equation on the complement of a divisor

Differential Geometry 2018-03-29 v1

Abstract

We consider the complex Monge-Amp\'{e}re equation on complete K\"{a}hler manifolds with cusp singularity along a divisor when the right hand side FF has rather weak regularity. We proved that when the right hand side FF is in some \emph{weighted} W1,p0W^{1,p_0} space for p0>2np_0 > 2n, the Monge-Amp\'{e}re equation has a classical W3,p0W^{3,p_0} solution.

Keywords

Cite

@article{arxiv.1803.10718,
  title  = {The complex Monge-Amp\'{e}re equation on the complement of a divisor},
  author = {Fangyu Zou},
  journal= {arXiv preprint arXiv:1803.10718},
  year   = {2018}
}
R2 v1 2026-06-23T01:07:59.527Z