Infinitely Many Pairs of Free Boundary Minimal Surfaces with the Same Topology and Symmetry Group

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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding="application/x-tex">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, three boundary components and antiprismatic symmetry group of order <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4 left-parenthesis g plus 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">4(g+1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.