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• W2567215999 abstract "For each integer $ggeq 1$ we use variational methods to construct in the unit $3$-ball $B$ a free boundary minimal surface $Sigma_g$ of symmetry group $mathbb{D}_{g+1}$. For $g$ large, $Sigma_g$ has three boundary components and genus $g$. As $grightarrowinfty$ the surfaces $Sigma_g$ converge as varifolds to the union of the disk and critical catenoid. These examples are the first with genus greater than $1$ and were conjectured to exist by Fraser-Schoen. We also construct several new free boundary minimal surfaces in $B$ with the symmetry groups of the cube, tetrahedron and dodecahedron. Finally, we prove that free boundary minimal surfaces isotopic to those of Fraser-Schoen can be constructed variationally using an equivariant min-max procedure. We also prove an $epsilon$-regularity theorem for free boundary minimal surfaces in $B$." @default.
• W2567215999 created "2017-01-06" @default.
• W2567215999 creator A5024143049 @default.
• W2567215999 date "2016-12-27" @default.
• W2567215999 modified "2023-09-27" @default.
• W2567215999 title "Free boundary minimal surfaces of unbounded genus" @default.
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