An existence time estimate for K\"ahler-Ricci flow

Albert Chau; Ka Fai Li; Luen-Fai Tam

An existence time estimate for K\"ahler-Ricci flow

Differential Geometry 2016-03-24 v2

Authors: Albert Chau , Ka Fai Li , Luen-Fai Tam

Abstract

Fix a complete noncompact \K manifold $(M^n,h_0)$ with bounded curvature. Let $g(t)$ be a bounded curvature solution to the \KR flow starting from some $g_0$ uniformly equivalent to $h_0$ . We estimate the existence time of $g(t)$ together with $C^0$ bounds and curvature bounds, where the estimates depend only on $h_0$ and the $C^0$ distance between $g_0$ and $h_0$ . We also generalize these results to cases when $g_0$ may have unbounded curvature.

Keywords

ricci flow mean curvature flow geometric flows

Cite

@article{arxiv.1508.03417,
  title  = {An existence time estimate for K\"ahler-Ricci flow},
  author = {Albert Chau and Ka Fai Li and Luen-Fai Tam},
  journal= {arXiv preprint arXiv:1508.03417},
  year   = {2016}
}

Comments

12 pages, minor corrections, proof of Theorem 2.3 modified, references updated

An existence time estimate for K\"ahler-Ricci flow

Abstract

Keywords

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