On the index of the critical M\"obius band in $\mathbb B^4$

Vladimir Medvedev

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arXiv · 2112.04883

On the index of the critical M\"obius band in $\mathbb B^4$

Vladimir Medvedev

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Abstract

In this paper we prove that the Morse index of the critical M\"obius band in the $4-$dimensional Euclidean ball $\mathbb B^4$ equals 5. It is conjectured that this is the only embedded non-orientable free boundary minimal surface of index 5 in $\mathbb B^4$. One of the ingredients in the proof is a comparison theorem between the spectral index of the Steklov problem and the energy index. The latter also enables us to give another proof of the well-known result that the index of the critical catenoid in $\mathbb B^3$ equals 4.

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Vladimir Medvedev. 2021-12-09. On the index of the critical M\"obius band in $\mathbb B^4$. https://arxiv.org/abs/2112.04883

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