English

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.

Keywords

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

R2 v1 2026-07-22T16:34:56.089Z