Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II

2019/03/11 by Gang Liu, Liu, Gang, Gábor Székelyhidi +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1903.04390

openalex created_date 2018/05/07 · openalex publication_date 2019/03/11 · openalex updated_date 2026/07/28

Abstract

We study non-collapsed Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below. Our main result is that each tangent cone is homeomorphic to a normal affine variety. This extends a result of Donaldson-Sun, who considered non-collapsed limits of polarized Kähler manifolds with two-sided Ricci curvature bounds.

Citations

• Regularity of Einstein manifolds and the codimension 4 conjecture
• On the parabolic kernel of the Schrödinger operator
• Differential equations on riemannian manifolds and their geometric applications
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
• L² Curvature Bounds on Manifolds with Bounded Ricci Curvature
• Existence and applications of Ricci flows via pseudolocality

Cited by

• Yang-Mills energy quantization over non-collapsed degenerating Einstein manifolds and applications
• Complete Kähler manifolds with nonnegative Ricci curvature II
• An ε-Regularity Theorem for Non-collapsed Ricci Flow
• Metric rigidity of Kahler manifolds with lower Ricci bounds and almost maximal volume
• An explicit estimate of the Bergman kernel for positive line bundles

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• On the tangent cone of Kähler manifolds with Ricci curvature lower bound
• Structure of spaces with Bakry-Émery Ricci curvature bounded below