Infinitely many pairs of free boundary minimal surfaces with the same topology and symmetry group

TL;DR

This paper constructs pairs of non-isometric free boundary minimal surfaces in the 3D unit ball that share the same topology and symmetry group, demonstrating non-uniqueness for large genus surfaces.

Contribution

It provides explicit examples of infinitely many pairs of free boundary minimal surfaces with identical topology and symmetry, expanding understanding of their classification.

Findings

Existence of pairs of non-isometric surfaces with same topology and symmetry

Surfaces have large genus, three boundary components, and specific symmetry group

Demonstrates non-uniqueness in free boundary minimal surfaces

Abstract

The topology and symmetry group of a free boundary minimal surface in the three-dimensional Euclidean unit ball do not determine the surface uniquely. We provide pairs of non-isometric free boundary minimal surfaces having any sufficiently large genus $g$, three boundary components and antiprismatic symmetry group of order $4(g+1)$.