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.
Dehn function, solvable group, lipschitz $1$-connectedness
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
22E25 - Nilpotent and solvable Lie groups