The Calabi flow on Kähler surfaces with bounded Sobolev constant. I

DOI10.1007/s00208-011-0723-7zbMath1254.53097arXiv0710.5159OpenAlexW2017136739MaRDI QIDQ453309

Xiuxiong Chen, Weiyong He

Publication date: 19 September 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.5159

zbMATH Keywords

curvature boundsCalabi flowtoric surfacesSobolev constantscalar flat bubblings

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Compact complex surfaces (32J15) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25)

Related Items (15)

Calabi flow on toric varieties with bounded Sobolev constant. I ⋮ A Concentration-Collapse Decomposition forL²Flow Singularities ⋮ On the extension and smoothing of the Calabi flow on complex tori ⋮ Local solution and extension to the Calabi flow ⋮ The long time behavior of fourth order curvature flows ⋮ Ambient obstruction flow ⋮ Regularity scales and convergence of the Calabi flow ⋮ Toric surfaces, \(K\)-stability and Calabi flow ⋮ The interior regularity of the Calabi flow on a toric surface ⋮ Kähler non-collapsing, eigenvalues and the Calabi flow ⋮ The gradient flow of the \(L^2\) curvature functional with small initial energy ⋮ A criterion for the properness of the \(K\)-energy in a general Kähler class ⋮ Kähler-Ricci flow, Kähler-Einstein metric, and K-stability ⋮ Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kähler metrics ⋮ Convergence of the Calabi flow on toric varieties and related Kähler manifolds

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