Applications conformes {\`a} grande {\'e}chelle
Differential Geometry
2017-11-28 v2 Metric Geometry
Abstract
Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated groups. Inspired by work by Benjamini and Schramm, we show that under such maps, some kind of dimension increases: exponent of volume growth for nilpotent groups, conformal dimension of the ideal boundary for hyperbolic groups. A purely metric space notion of {\ell} p-cohomology plays a key role.
Cite
@article{arxiv.1604.01195,
title = {Applications conformes {\`a} grande {\'e}chelle},
author = {Pierre Pansu},
journal= {arXiv preprint arXiv:1604.01195},
year = {2017}
}
Comments
New version stresses that results apply to coarse embeddings and includes a reference to recent work by Hume-Mackay-Tessera