Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below

Gang Liu, Gábor Székelyhidi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We show that non-collapsed Gromov–Hausdorff limits of polarized Kähler manifolds, with Ricci curvature bounded below, are normal projective varieties, and the metric singularities of the limit space are precisely given by a countable union of analytic subvarieties. This extends a fundamental result of Donaldson–Sun, in which 2-sided Ricci curvature bounds were assumed. As a basic ingredient we show that, under lower Ricci curvature bounds, almost Euclidean balls in Kähler manifolds admit good holomorphic coordinates. Further applications are integral bounds for the scalar curvature on balls, and a rigidity theorem for Kähler manifolds with almost Euclidean volume growth.

Original languageEnglish (US)
Pages (from-to)236-279
Number of pages44
JournalGeometric and Functional Analysis
Volume32
Issue number2
DOIs
StatePublished - Apr 2022

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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