On a class of fully nonlinear flow in Kähler geometry

2009/04/21 by Fang, Hao, Lai, Mijia, Ma, Xinan · 3 citations
#53C44 #53C55 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.3288

Abstract

In this paper, we study a class of fully nonlinear metric flow 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 solved 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.

Cited by

• Fully non-linear elliptic equations on noncompact complex manifolds
• The Critical LYZ equation in Kähler Geometry
• A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds

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