English

The Calabi flow on toric Fano surface

Differential Geometry 2009-12-24 v4 Analysis of PDEs

Abstract

We prove the longtime existence and convergence of the Calabi flow on toric Fano surfaces in a large family of Kahler classes where the class has positive extremal Hamiltonian potential and the initial Calabi energy is bounded by some constant. This is an extension of our previous work. We use the toric condition in a more essential way to rule out bubbles.

Keywords

Cite

@article{arxiv.0807.3984,
  title  = {The Calabi flow on toric Fano surface},
  author = {Xiuxiong Chen and Weiyong He},
  journal= {arXiv preprint arXiv:0807.3984},
  year   = {2009}
}

Comments

Some errors are corrected and Section 3 is thoroughly rewritten

R2 v1 2026-06-21T11:04:08.041Z