Jacob Bernstein

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20232026

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math.DG2026

Willmore energy and minimal fillings

Jacob Bernstein, Daniel Ketover

For each $n \geq 4$ , we show that the infimal Willmore energy of a non-orientable surface of odd genus immersed in $S^{n}$ is attained by an index $(n + 1)$ minimal surface in…

math.DG2026

Minimal equatorial fillings of low index

Jacob Bernstein, Daniel Ketover

We obtain restrictions on the geometry and topology of minimal equatorial fillings in $S^{3}$ of the lowest possible Morse index.

math.DG2026

On the Willmore energy of Möbius bands

Jacob Bernstein, Daniel Ketover

We show that among Möbius bands in $S^{3}$ bounded by a great circle, the minimal Willmore energy is realized by an embedded minimal Möbius band with Morse index two. To pro…

math.DG2026

Minimal equatorial fillings

Jacob Bernstein, Daniel Ketover

We show that a great circle in $S^{3}$ bounds embedded non-orientable minimal surfaces of unbounded genera and all possible non-zero Euler numbers. This answers a question o…

math.DG2026

Orientable minimal submanifolds of low index in the sphere

Jacob Bernstein, Daniel Ketover

In this short note we prove a rigidity result for orientable minimal submanifolds in the round sphere of the lowest non-trivial Morse index. In particular, we show that the only cl…