Uniqueness and short time regularity of the weak Kähler-Ricci flow

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• 作者：Eleonora Di Nezza^a ; ^{e.di-nezza@imperial.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Chinh H. Lu^b ; ¹ ; ^{chinh@chalmers.se" class="auth_mail" title="E-mail the corresponding author} ; ^{hoang-chinh.lu@math.u-psud.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Kä ; hler-Ricci flow ; Monge&ndash ; Ampè ; re equation ; Lelong number ; Quasi plurisubharmonic function ; Generalized capacity
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：305
• 期：Complete
• 页码：953-993
• 全文大小：626 K

文摘

Let X   be a compact Kähler manifold. We prove that the Kähler–Ricci flow starting from arbitrary closed positive (1,1)$(1,1)$-currents is smooth outside some analytic subset. This regularity result is optimal, meaning that the flow has positive Lelong numbers for short time if the initial current has. We also prove that the flow is unique when starting from currents with zero Lelong numbers.