Contracting thin disks

Abstract

We answer a question of Liokumovich-Nabutovsky-Rotman showing that if D is a Riemannian 2-disc with boundary length L, diameter d and area A << d then D can be filled by a homotopy where the lengths of the intermediate curves are bounded by $L+2d+O(\sqrt{A})$.

6 pages, revised the questions section

References in corpus (2)

• Diastolic and isoperimetric inequalities on surfaces
• Contracting the boundary of a Riemannian 2-disc