English

On stability and the convergence of the K\"ahler-Ricci flow

Differential Geometry 2007-05-23 v1 Analysis of PDEs

Abstract

Assuming uniform bounds for the curvature, the exponential convergence of the K\"ahler-Ricci flow is established under two conditions which are a form of stability: the Mabuchi energy is bounded from below, and the dimension of the space of holomorphic vector fields in an orbit of the diffeomorphism group cannot jump up in the limit.

Keywords

Cite

@article{arxiv.math/0412185,
  title  = {On stability and the convergence of the K\"ahler-Ricci flow},
  author = {D. H. Phong and Jacob Sturm},
  journal= {arXiv preprint arXiv:math/0412185},
  year   = {2007}
}

Comments

18 pages, no figure