Volume 24, issue 3 (2020)

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Pluripotential Kähler–Ricci flows

Vincent Guedj, Chinh H Lu and Ahmed Zeriahi

Geometry & Topology 24 (2020) 1225–1296

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.

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parabolic Monge–Ampère equation, pluripotential solution, Perron envelope, Kähler–Ricci flow
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 32W20, 58J35
Received: 7 November 2018
Revised: 12 August 2019
Accepted: 23 September 2019
Published: 30 September 2020
Proposed: Simon Donaldson
Seconded: John Lott, Bruce Kleiner
Vincent Guedj
Institut de Mathématiques de Toulouse
Université de Toulouse, CNRS
Chinh H Lu
Laboratoire de Mathématiques d’Orsay
Univ. Paris-Sud, CNRS, Université Paris-Saclay
Ahmed Zeriahi
Institut de Mathématiques de Toulouse
Université de Toulouse, CNRS