On a class of fully nonlinear flows in Kähler geometry

On a class of fully nonlinear flows in Kähler geometry

In this paper, we study a class of fully nonlinear metric flows on Kähler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for the long time convergence of the flow, generalizing the result of Song–Weinkove. As a consequence, under the given con...

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Veröffentlicht in:Journal für die reine und angewandte Mathematik 2011-04, Vol.2011 (653), p.189-220
Hauptverfasser: Fang, Hao, Lai, Mijia, Ma, Xinan
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Lai, Mijia
Ma, Xinan
description In this paper, we study a class of fully nonlinear metric flows on Kähler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for the long time convergence of the flow, generalizing the result of Song–Weinkove. As a consequence, under the given condition, we solve the corresponding Euler equation, which is fully nonlinear of Monge–Ampère type. As an application, we also discuss a complex Monge–Ampère type equation including terms of mixed degrees, which was first posed by Chen.
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title On a class of fully nonlinear flows in Kähler geometry
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