Convergence of the Kähler–Ricci iteration

Darvas, Tamás; Rubinstein, Yanir A.

doi:10.2140/apde.2019.12.721

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

Convergence of the Kähler–Ricci iteration

Tamás Darvas and Yanir A. Rubinstein

Vol. 12 (2019), No. 3, 721–735

DOI: 10.2140/apde.2019.12.721

Abstract

The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Ricci flow converges to a Kähler–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

Ricci iteration, Kähler–Einstein metrics, Fano manifolds

Mathematical Subject Classification 2010

Primary: 32Q20

Secondary: 14J45, 32W20

Milestones

Received: 15 June 2017

Revised: 27 April 2018

Accepted: 29 June 2018

Published: 7 October 2018

Authors

Tamás Darvas
Department of Mathematics University of Maryland College Park, MD United States

Yanir A. Rubinstein
Department of Mathematics University of Maryland College Park, MD United States

Vol. 12, No. 3, 2019