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Geometry & Topology
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arXiv.org e-Print Archive
Preprint . 2018
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Pluripotential Kähler–Ricci flows

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type , Report 30 Sep 2020Embargo end date: 01 Jan 2018 English Publisher:Mathematical Sciences PublishersJournal:Geometry & Topology, volume 24, pages 1,225-1,296 (issn: 1465-3060, eissn: 1364-0380, Copyright policy )
Authors: Guedj, Vincent; Lu, Chinh H.; Zeriahi, Ahmed;

doi: 10.2140/gt.2020.24.1225 , 10.48550/arxiv.1810.02121

arXiv: http://arxiv.org/abs/1810.02121

Pluripotential Kähler–Ricci flows

Abstract

We develop a parabolic pluripotential theory on compact K{��}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{��}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{��}hler-Ricci flow on varieties with log terminal singularities.

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Keywords

Mathematics - Differential Geometry, Mathematics - Complex Variables, parabolic Monge–Ampère equation, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], pluripotential solution, Perron envelope, 53C44, 510, Mathematics - Analysis of PDEs, 58J35, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Kähler–Ricci flow, 32W20, Complex Variables (math.CV), Analysis of PDEs (math.AP)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Top 10%
Average
Top 10%
Green
bronze