English

On a conjecture of Cheeger

Metric Geometry 2016-08-08 v2

Abstract

This note details how a recent structure theorem for normal 11-currents proved by the first and third author allows to prove a conjecture of Cheeger concerning the structure of Lipschitz differentiability spaces. More precisely, we show that the push-forward of the measure from a Lipschitz differentiability space under a chart is absolutely continuous with respect to Lebesgue measure.

Keywords

Cite

@article{arxiv.1607.02554,
  title  = {On a conjecture of Cheeger},
  author = {Guido De Philippis and Andrea Marchese and Filip Rindler},
  journal= {arXiv preprint arXiv:1607.02554},
  year   = {2016}
}

Comments

Final version with minor revisions

R2 v1 2026-06-22T14:49:48.104Z