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For any compact surface $\Sigma$ with smooth, non-empty boundary, weconstruct a free boundary minimal immersion into a Euclidean Ball$\mathbb{B}^N$ where $N$ is controlled in terms of the topology of $\Sigma$. Weobtain these as maximizing metrics for the isoperimetric problem for the firstnon-trivial Steklov eigenvalue. Our main technical result concerns asymptoticcontrol on eigenvalues in a delicate glueing construction which allows us toprove the remaining spectral gap conditions to complete the program byFraser--Schoen and the second named author to obtain such mazimizing metrics.Our construction draws motivation from earlier work by the first named authorwith Siffert on the corresponding problem in the closed case.

Free boundary minimal surfaces of any topological type in Euclidean balls via shape optimization