From almost smooth spaces to RCD spaces

TL;DR

This paper characterizes almost smooth spaces as RCD spaces using local volume doubling and Poincaré inequalities, with applications to Einstein 4-orbifolds.

Contribution

It introduces new characterizations of RCD spaces based on local geometric and analytic conditions, extending understanding of their structure.

Findings

Characterization of RCD spaces via volume doubling and Poincaré inequalities

Application to Einstein 4-orbifolds classification

New criteria for almost smooth spaces to be RCD spaces

Abstract

We provide various characterizations for a given almost smooth space to be an RCD space, in terms of a local volume doubling and a local Poincar\'e inequality. Applications include a characterization of Einstein $4$-orbifolds.