Weakly non-collapsed RCD spaces are strongly non-collapsed

Camillo Brena, Nicola Gigli, Shouhei Honda, Xingyu Zhu

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second named author in full generality. One of the auxiliary results of independent interest that we obtain is about the link between the properties tr (Hess f) = Δ f on U ⊆ X for every f sufficiently regular, m = c H n on U ⊆ X for some c > 0, where U ⊆ X is open and X is a - possibly collapsed - RCD space of essential dimension n.

Original languageEnglish
Pages (from-to)215-252
Number of pages38
JournalJournal fur die Reine und Angewandte Mathematik
Issue number794
Publication statusPublished - 2023 Jan 1


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