English

Convergence of the K\"ahler-Ricci iteration

Differential Geometry 2021-12-03 v1 Analysis of PDEs Complex Variables

Abstract

The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Ricci flow converges to a Kahler-Einstein metric whenever one exists, and it has been conjectured that the Ricci iteration should behave similarly. This article confirms this conjecture. As a special case, this gives a new method of uniformization of the Riemann sphere.

Keywords

Cite

@article{arxiv.1705.06253,
  title  = {Convergence of the K\"ahler-Ricci iteration},
  author = {Tamás Darvas and Yanir A. Rubinstein},
  journal= {arXiv preprint arXiv:1705.06253},
  year   = {2021}
}