Kähler non-collapsing, eigenvalues and the Calabi flow

Abstract

We first proved a compactness theorem of the Kähler metrics, which confirms a prediction of Chen. Then we prove several eigenvalue estimates along the Calabi flow. Combining the compactness theorem and these eigenvalue estimates, we generalize the method developed by Chen-Li-Wang to prove the small energy theorems of the Calabi flow.

33 pages, final version, to appear in Journal of Functional Analysis

References in corpus (6)

• Interior estimates for solutions of Abreu's equation
• Space of Kähler metrics (IV)--On the lower bound of the K-energy
• The global existence and convergence of the Calabi flow on ${\mathbb{C}}^n/{\mathbb{Z}}^n+i{\mathbb{Z}}^n$
• Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds
• Remark on the Calabi flow with bounded curvature
• The interior regularity of the Calabi flow on a toric surface

Cited by in corpus (3)

• Regularity scales and convergence of the Calabi flow
• $I$-properness of Mabuchi's $K$-energy
• Generalized Matsushima's theorem and Kähler-Einstein cone metrics