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

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arxiv 2205.04861 v3 pith:U7YDDRUK submitted 2022-05-10 math.DG math.AP

Alessandro Carlotto , Mario B. Schulz , David Wiygul This is my paper
classification math.DGmath.AP
keywords boundaryfreegroupminimalsymmetrypairssurfacesurfaces
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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 $4(g+1)$.

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  1. A new family of minimal surfaces of even genus in the three-dimensional sphere

    math.DG 2025-07 conditional novelty 7.0 of 10

    For each n at least 2, an equivariant min-max procedure yields a new embedded minimal surface Gamma_n in S^3 with genus 2n or 2n-2, area just above the sphere's, full symmetry group G_n for n at least 4, and Morse ind...

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