The compactness result for Kähler Ricci solitons

2005/04/26 by Huai-Dong Cao, Cao, Huai-Dong, Natasa Sesum +1
Mathematics · #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C44

paper · pdf · doi:10.48550/arxiv.math/0504526

arxiv created 2005/09/21 · arxiv updated 2009/12/01

Abstract

In this paper we prove the compactness result for compact Kähler Ricci gradient shrinking solitons. If (M_i,g_i) is a sequence of Kähler Ricci solitons of real dimension n ≥ 4, whose curvatures have uniformly bounded L^n/2 norms, whose Ricci curvatures are uniformly bounded from below and μ(g_i,1/2) ≥ A (where μ is Perelman's functional), there is a subsequence (M_i,g_i) converging to a compact orbifold (M_∞,g_∞) with finitely many isolated singularitites, where g_∞ is a Kähler Ricci soliton metric in an orbifold sense (satisfies a soliton equation away from singular points and smoothly extends in some gauge to a metric satisfying Kähler Ricci soliton equation in a lifting around singular points).

Related

• A compactness theorem for four-dimensional shrinking gradient Ricci solitons
• Topological Obstructions to the Existence of Compact Shrinking Ricci Solitons in Dimension Four
• Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
• Rigidity of four-dimensional Kähler-Ricci solitons
• Convergence of compact Ricci solitons