Free boundary minimal M\"obius bands in toroids

TL;DR

This paper demonstrates the existence of infinitely many embedded free boundary minimal M"obius bands and annuli in strictly mean convex toroids, constructed via equivariant variational methods with areas proportional to their symmetry group order.

Contribution

It introduces a novel construction of free boundary minimal surfaces in toroids, expanding the known family of such surfaces with infinitely many examples.

Findings

Existence of infinitely many embedded free boundary minimal M"obius bands in toroids.

Existence of infinitely many embedded free boundary minimal annuli in toroids.

Surface areas grow linearly with symmetry group order.

Abstract

We prove that strictly mean convex toroids contain infinitely many (geometrically distinct) embedded free boundary minimal M\"obius bands as well as infinitely many embedded free boundary minimal annuli. The surfaces in both families are constructed by means of equivariant variational methods and their areas grow linearly with the order of their symmetry groups.