An existence time estimate for Kähler-Ricci flow

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.

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

References in corpus (4)

• Interior derivative estimates for the Kähler-Ricci flow
• Deforming complete Hermitian metrics with unbounded curvature
• Kähler-Ricci flow with unbounded curvature
• Longtime existence of the Kähler-Ricci flow on ${\mathbb{C}}^n$