Free Boundary Minimal Annuli Immersed in the Unit 3-Ball

TL;DR

This paper constructs a new family of free boundary minimal annuli in the unit 3-ball using PDE gluing, featuring equatorial disks connected by half-catenoidal bridges, advancing understanding of minimal surface configurations.

Contribution

It introduces a PDE gluing method to produce non-rotational free boundary minimal annuli, expanding the known examples in the Euclidean unit 3-ball.

Findings

Constructed a discrete family of minimal annuli

Surfaces resemble disks joined by catenoidal bridges

Method advances minimal surface theory

Abstract

Using the linearized doubling methodology we carry out a PDE gluing construction of a discrete family of non-rotational properly immersed free boundary minimal annuli in the Euclidean unit 3-ball. The surfaces we construct resemble equatorial disks joined by half-catenoidal bridges at the boundary.