Free boundary minimal disks in convex balls

Author:

Robert Haslhofer, Daniel Ketover

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP), Geometric Topology (math.GT)

journal:

date:

2023-07-03 16:00:00

Abstract

In this paper, we prove that every strictly convex 3-ball with nonnegative Ricci-curvature contains at least 3 embedded free-boundary minimal 2-disks for any generic metric, and at least 2 solutions even without genericity assumption. Our approach combines ideas from mean curvature flow, min-max theory and degree theory. We also establish the existence of smooth free-boundary mean-convex foliations. In stark contrast to our prior work in the closed setting, the present result is sharp for generic metrics.

PDF: Free boundary minimal disks in convex balls.pdf