The conical K\"ahler-Ricci flow on Fano manifolds
Differential Geometry
2015-02-03 v3
Abstract
In this paper, we study the long-term behavior of the conical K\"ahler-Ricci flow on Fano manifold . First, based on our work of locally uniform regularity for the twisted K\"ahler-Ricci flows, we obtain a long-time solution to the conical K\"ahler-Ricci flow by limiting a sequence of these twisted flows. Second, we study the uniform Perelman's estimates of the twisted K\"ahler-Ricci flows. After that, we prove that the conical K\"ahler-Ricci flow must converge to a conical K\"ahler-Einstein metric if there exists one.
Keywords
Cite
@article{arxiv.1402.1832,
title = {The conical K\"ahler-Ricci flow on Fano manifolds},
author = {Jiawei Liu and Xi Zhang},
journal= {arXiv preprint arXiv:1402.1832},
year = {2015}
}
Comments
46 pages