English

Local solution and extension to the Calabi flow

Differential Geometry 2009-04-19 v2 Analysis of PDEs

Abstract

We consider the local solution to the Calabi flow for C^\alpha initial metric. We also prove that the Calabi flow on compact Kaehler surfaces can be extended once the metrics along the flow are bounded in L^\infty sense. This can be viewed as obtaining higher order derivative estimates from second order derivatives for a fourth order nonlinear equation.

Keywords

Cite

@article{arxiv.0904.0978,
  title  = {Local solution and extension to the Calabi flow},
  author = {Weiyong He},
  journal= {arXiv preprint arXiv:0904.0978},
  year   = {2009}
}

Comments

11 pages; Proof of Theorem 2.1 is rewritten

R2 v1 2026-06-21T12:48:44.776Z