Lipschitz 1-connectedness for Some Solvable Lie Groups

Abstract

AbstractA space X is said to be Lipschitz 1-connected if every Lipschitz loop 𝛾 : S 1 → X bounds a O (Lip(𝛾))-Lipschitz disk f : D 2 → X. 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.