# Existence and classification of $S^1$-invariant free boundary annuli and Möbius bands in $\mathbb{B}^n$

@article{Fraser2019ExistenceAC, title={Existence and classification of \$S^1\$-invariant free boundary annuli and M{\"o}bius bands in \$\mathbb\{B\}^n\$}, author={Ailana M. Fraser and Pam Sargent}, journal={arXiv: Differential Geometry}, year={2019} }

We explicitly classify all $S^1$-invariant free boundary minimal annuli and Mobius bands in $\mathbb{B}^n$. This classification is obtained from an analysis of the spectrum of the Dirichlet-to-Neumann map for $S^1$-invariant metrics on the annulus and Mobius band. First, we determine the supremum of the $k$-th normalized Steklov eigenvalue among all $S^1$-invariant metrics on the Mobius band for each $k \geq 1$, and show that it is achieved by the induced metric from a free boundary minimal…

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