Lipschitz 1-connectedness for some solvable Lie groups

TL;DR

This paper proves that certain solvable Lie groups with quadratic isoperimetric inequalities are also Lipschitz 1-connected, establishing a link between geometric properties and group structure.

Contribution

The authors extend previous results by Cornulier and Tessera, demonstrating that specific solvable Lie groups are Lipschitz 1-connected, a property previously known to imply quadratic isoperimetric inequalities.

Findings

Certain solvable Lie groups are Lipschitz 1-connected

Lipschitz 1-connectedness implies quadratic isoperimetric inequality

Extension of previous results by Cornulier and Tessera

Abstract

A space X is said to be Lipschitz 1-connected if every L-Lipschitz loop in X bounds a O(L)-Lipschitz disk. A Lipschitz 1-connected space admits a quadratic isoperimetric inequality, but it is unknown whether the converse is true. Cornulier and Tessera showed that certain solvable Lie groups have quadratic isoperimetric inequalities, and we extend their result to show that these groups are Lipschitz 1-connected.