Weak solutions to degenerate complex Monge-Ampère flows II

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• 作者：Philippe Eyssidieux^a ; ^b ; ^{Philippe.Eyssidieux@ujf-grenoble.fr" class="auth_mail" title="E-mail the corresponding author} ; Vincent Guedj^c ; ^b ; ^{vincent.guedj@math.univ-toulouse.fr" class="auth_mail" title="E-mail the corresponding author} ; Ahmed Zeriahi^c ; ^{zeriahi@math.univ-toulouse.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Complex Monge&ndash ; Ampè ; re flows ; Kä ; hler&ndash ; Ricci flow ; Canonical singularities ; Viscosity solutions
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：30 April 2016
• 年：2016
• 卷：293
• 期：Complete
• 页码：37-80
• 全文大小：714 K

文摘

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.