Free boundary saddle disks in the unit ball

TL;DR

This paper constructs an infinite family of non-planar free boundary disks with non-positive Gaussian curvature within the unit ball in three-dimensional space, expanding the understanding of minimal surface configurations.

Contribution

It introduces a new class of free boundary minimal disks with non-positive Gaussian curvature in the unit ball, which were not previously known.

Findings

Existence of infinite family of such disks.

Disks have non-positive Gaussian curvature.

Disks are non-planar and satisfy free boundary conditions.

Abstract

We construct an infinite family of non-planar free boundary disks of non-positive Gaussian curvature in the unit ball of $\mathbb{R}^3$.