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arXiv · 2609.26701

Minimal equatorial fillings

Jacob Bernstein·Daniel Ketover
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Abstract

We show that a great circle in $\mathbb{S}^3$ bounds embedded non-orientable minimal surfaces of unbounded genera and all possible non-zero Euler numbers. This answers a question of R. Hardt and H. Rosenberg (1990). It also gives the first example of a real analytic Jordan curve bounding infinitely many embedded minimal surfaces of distinct topological types. Such surfaces may arise as the links of boundary singularities of non-orientable minimal hypersurfaces in $\mathbb{R}^4$.

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Jacob Bernstein, Daniel Ketover. 2026-09-22. Minimal equatorial fillings. https://arxiv.org/abs/2609.26701

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