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

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 $4(g+1)$.Comment: final preprint version, to appear in Memoirs of the American Mathematical Societ