Collapsing geometry with RICCI curvature bounded below and RICCI flow smoothing

Shaosai Huang, Xiaochun Rong, Bing Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques. We then prove that if a Calabi–Yau manifold is sufficiently volume collapsed with bounded diameter and sectional curvature, then it admits a Ricci-flat Kähler metric together with a compatible pure nilpotent Killing structure: this is related to an open question of Cheeger, Fukaya and Gromov.

Original languageEnglish (US)
Article number123
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume16
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

Keywords

  • Almost flat manifold
  • Collapsing geometry
  • Locally bounded Ricci covering geometry
  • Nilpotent Killing structure
  • Ricci flow

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