Collapsed manifolds with ricci bounded covering geometry

HONGZHI HUANG, LINGLING KONG, XIAOCHUN RONG, SHICHENG XU

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5 Scopus citations

Abstract

We study collapsed manifolds with Ricci bounded covering geometry, i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform Reifenberg points. Applying the techniques in the Ricci flow, we partially extend the nilpotent structural results of Cheeger-Fukaya-Gromov, on the collapsed manifolds with (sectional curvature) local bounded covering geometry, to the manifolds with (global) Ricci bounded covering geometry.

Original languageEnglish (US)
Pages (from-to)8039-8057
Number of pages19
JournalTransactions of the American Mathematical Society
Volume373
Issue number11
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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