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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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On a class of fully nonlinear flows in Kähler geometry

1Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA 52240, USA

2Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui Province, China

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2011, Issue 653, Pages 189–220, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2011.027, January 2011

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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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