Lipschitz connectivity and filling invariants in solvable groups and buildings

TL;DR

This paper introduces new Lipschitz extension techniques to bound filling invariants in nonpositively curved spaces, providing sharp bounds for higher-order Dehn functions in various geometric and algebraic structures.

Contribution

It develops novel methods based on Lipschitz extension theorems to estimate filling invariants, improving understanding of geometric group theory in complex spaces.

Findings

Sharp bounds on higher-order Dehn functions of Sol_{2n+1}

Bounds on filling invariants of horospheres in Euclidean buildings

Results on S-arithmetic groups and Hilbert modular groups

Abstract

We give some new methods, based on Lipschitz extension theorems, for bounding filling invariants of subsets of nonpositively curved spaces. We apply our methods to find sharp bounds on higher-order Dehn functions of Sol_{2n+1}, horospheres in euclidean buildings, Hilbert modular groups, and certain S-arithmetic groups.