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arXiv · 2509.12823

Dehn functions: computations, lower bounds, and the quasiisometric rigidity of $\rm{Sol}_5$

Ido Grayevsky·Gabriel Pallier
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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 $\rm{Sol}_5$ 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 $5$, which we compute using Cornulier and Tessera's results.

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BibTeXRIS

Ido Grayevsky, Gabriel Pallier. 2025-09-16. Dehn functions: computations, lower bounds, and the quasiisometric rigidity of $\rm{Sol}_5$. https://arxiv.org/abs/2509.12823

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