Weak solutions to degenerate complex Monge–Ampère flows II

Studying the (long-term) behavior of the Kähler–Ricci flow on mildly singular varieties, one is naturally led to study weak solutions of degenerate parabolic complex Monge–Ampère equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for dege...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 293; pp. 37 - 80
Main Authors Eyssidieux, Philippe, Guedj, Vincent, Zeriahi, Ahmed
Format Journal Article
LanguageEnglish
Published Elsevier Inc 30.04.2016
Elsevier
Subjects
Canonical singularities
Complex Monge–Ampère flows
Complex Variables
Differential Geometry
Kähler–Ricci flow
Mathematics
Viscosity solutions
Kähler–Ricci flow
Canonical singularities
Complex Monge–Ampère flows
Viscosity solutions
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ISSN0001-8708
1090-2082
1090-2082
DOI10.1016/j.aim.2016.02.010

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Summary:Studying the (long-term) behavior of the Kähler–Ricci flow on mildly singular varieties, one is naturally led to study weak solutions of degenerate parabolic complex Monge–Ampère equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Monge–Ampère flows on compact Kähler manifolds. Our general theory allows in particular to define and study the (normalized) Kähler–Ricci flow on varieties with canonical singularities, generalizing results of Song and Tian.
ISSN:0001-8708
1090-2082
1090-2082
DOI:10.1016/j.aim.2016.02.010