A new parabolic flow in Kaehler manifolds
Differential Geometry
2007-05-23 v2
Abstract
In this paper, we introduce a new parabolic equation on K\"ahler manifolds. The static point of this flow is related to the existence of a lower bound of the Mabuchi energy. In this paper, we prove the flow always exists for all times for any initial smooth data. Further more, if the initial metric has non-negative bisectional curvature, we prove the flow converges to a static metric eventually.
Cite
@article{arxiv.math/0009247,
title = {A new parabolic flow in Kaehler manifolds},
author = {Xiuxiong Chen},
journal= {arXiv preprint arXiv:math/0009247},
year = {2007}
}
Comments
15 pages, only one sentence was changed, to appear in CAG