New differential operator and noncollapsed rcd spaces

Research output: Contribution to journalArticlepeer-review

Abstract

We show characterizations of noncollapsed compact RCD(K; N ) spaces, which in particular confirm a conjecture of De Philippis and Gigli on the implication from the weakly noncollapsed condition to the noncollapsed one in the compact case. The key idea is to give the explicit formula of the Laplacian associated to the pullback Riemannian metric by embedding in L2 via the heat kernel. This seems to be the first application of geometric flow to the study of RCD spaces.

Original languageEnglish
Pages (from-to)2127-2148
Number of pages22
JournalGeometry and Topology
Volume24
Issue number4
DOIs
Publication statusPublished - 2020

ASJC Scopus subject areas

  • Geometry and Topology

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