Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold

2018/06/12 by Laurain, Paul, Petrides, Romain · 1 citation
#35J47 #35R35 #58E12 #58E20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.04665

Abstract

We perform a replacement procedure in order to produce a free boundary minimal surface whose area achieves the min-max value over all disk sweepouts of a manifold whose boundary lie in a submanifold. Our result is based on a proof of the convexity of the energy for free boundary harmonic maps and a generalization of Colding-Minicozzi replacement procedure.

Cited by

• Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds

Related

• On the free boundary min-max geodesics
• Min-max free boundary minimal surface with genus at least one
• Multiplicity one for min-max theory in compact manifolds with boundary and its applications
• Locally Maximizing Metric of Width on Manifolds with Boundary
• Rigidity of area-minimizing free boundary surfaces in mean convex\n three-manifolds