On a class of fully nonlinear flow in K\"ahler geometry
Differential Geometry
2010-02-24 v2 Analysis of PDEs
Abstract
In this paper, we study a class of fully nonlinear metric flow on K\"ahler 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-Amp\`ere type. As an application, we also discuss a complex Monge-Amp\`ere type equation including terms of mixed degrees, which was first posed by Chen.
Cite
@article{arxiv.0904.3288,
title = {On a class of fully nonlinear flow in K\"ahler geometry},
author = {Hao Fang and Mijia Lai and Xinan Ma},
journal= {arXiv preprint arXiv:0904.3288},
year = {2010}
}
Comments
Added the second Appendix, some minor mistakes corrected. To appear in Crelle's Journal