The first $p$-widths of the unit disk

Abstract

On compact 2-manifolds with non-empty convex boundary, we prove a regularity result for integral 1-varifolds $V$ that are stationary with free boundary and ${\mathbb{Z}}_2$-almost minimizing in small annuli. That regularity says that $V$ is a free boundary finite geodesic network. Next, using that regularity, we compute the first $p$-widths of the unit closed ball $B^2,$ for $p=1,...,4.$

34 pages, 15 figures

References in corpus (3)

• Nonpersistence of resonant caustics in perturbed elliptic billiards
• On the Multiplicity One Conjecture in Min-max theory
• The p-widths of a surface