The K\"ahler-Ricci flow and the $\bar\partial$ operator on vector fields
Differential Geometry
2018-12-20 v2 Complex Variables
Abstract
The limiting behavior of the normalized K\"ahler-Ricci flow for manifolds with positive first Chern class is examined under certain stability conditions. First, it is shown that if the Mabuchi K-energy is bounded from below, then the scalar curvature converges uniformly to a constant. Second, it is shown that if the Mabuchi K-energy is bounded from below and if the lowest positive eigenvalue of the operator on smooth vector fields is bounded away from 0 along the flow, then the metrics converge exponentially fast in to a K\"ahler-Einstein metric.
Cite
@article{arxiv.0705.4048,
title = {The K\"ahler-Ricci flow and the $\bar\partial$ operator on vector fields},
author = {D. H. Phong and Jian Song and Jacob Sturm and Ben Weinkove},
journal= {arXiv preprint arXiv:0705.4048},
year = {2018}
}