English

Weak solutions to degenerate complex Monge-Amp\'ere Flows II

Complex Variables 2014-07-10 v1 Analysis of PDEs Differential Geometry

Abstract

Studying the (long-term) behavior of the K\"ahler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Amp\'ere equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Monge-Amp\'ere flows on compact K\"ahler manifolds. Our general theory allows in particular to define and study the (normalized) K\"ahler-Ricci flow on varieties with canonical singularities, generalizing results of Song and Tian.

Keywords

Cite

@article{arxiv.1407.2504,
  title  = {Weak solutions to degenerate complex Monge-Amp\'ere Flows II},
  author = {Philippe Eyssidieux and Vincent Guedj and Ahmed Zeriahi},
  journal= {arXiv preprint arXiv:1407.2504},
  year   = {2014}
}
R2 v1 2026-06-22T04:59:38.499Z