Mathematics

Non-collapsed RCD spaces, i.e. RCD(K,N) spaces where the reference measure is exactly H^N exhibit a particularly regular behavior. Honda proved, in the compact case, that if an RCD(K,N) space is weakly non-collapsed (i.e. its reference measure is absolutely continuous with respect to H^N) then the space is actually non-collapsed, as conjectured by De Philippis and Gigli. The aim of this talk is to extend Honda’s result to possibly non-compact RCD spaces and present some result of independent interest used in the proof.