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Pluripotential Kähler–Ricci flows

Vincent Guedj, Chinh H Lu and Ahmed Zeriahi

Geometry & Topology 24 (2020) 1225–1296
Abstract

We develop a parabolic pluripotential theory on compact Kähler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge–Ampère equations. We provide a parabolic analogue of the celebrated Bedford–Taylor theory and apply it to the study of the Kähler–Ricci flow on varieties with log terminal singularities.

Keywords
parabolic Monge–Ampère equation, pluripotential solution, Perron envelope, Kähler–Ricci flow
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 32W20, 58J35
References
Publication
Received: 7 November 2018
Revised: 12 August 2019
Accepted: 23 September 2019
Published: 30 September 2020
Proposed: Simon Donaldson
Seconded: John Lott, Bruce Kleiner
Authors
Vincent Guedj
Institut de Mathématiques de Toulouse
Université de Toulouse, CNRS
Toulouse
France
https://www.math.univ-toulouse.fr/~guedj/
Chinh H Lu
Laboratoire de Mathématiques d’Orsay
Univ. Paris-Sud, CNRS, Université Paris-Saclay
Orsay
France
https://www.math.u-psud.fr/~lu/
Ahmed Zeriahi
Institut de Mathématiques de Toulouse
Université de Toulouse, CNRS
Toulouse
France
https://www.math.univ-toulouse.fr/~zeriahi/