Dehn functions: computations, lower bounds, and the quasiisometric rigidity of $\rm{Sol}_5$
Abstract
We establish distortion estimates in completely solvable Lie groups, using a sublinear bilipschitz retraction constructed by Cornulier, and interpolating between two theorems of Osin. This provides new lower bounds on Dehn functions. Our second main result is the quasiisometric rigidity of and its lattices. Together with a theorem of Peng, a key tool for the rigidity is the complete list of Dehn functions and dimensions of asymptotic cones of all simply connected solvable Lie groups of exponential growth up to dimension , which we compute using Cornulier and Tessera's results.
Keywords
Cite
@article{arxiv.2509.12823,
title = {Dehn functions: computations, lower bounds, and the quasiisometric rigidity of $\rm{Sol}_5$},
author = {Ido Grayevsky and Gabriel Pallier},
journal= {arXiv preprint arXiv:2509.12823},
year = {2025}
}
Comments
34 pages, 5 tables, 2 figures. The contents of this preprint is a revised form of the second part of arXiv:2410.0542v1, which was split in two parts by the authors. The first part was updated as a new version at arXiv:2410.0542