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Abstract
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.
Received: 2009-05-26
Revised: 2009-12-22
Published Online: 2011-01-12
Published in Print: 2011-April
© Walter de Gruyter Berlin · New York 2011
