For every half-integer J and sufficiently large integer m, the authors construct an embedded self-shrinker with 2J+1 ends and genus 2J(m-1) by gluing stacked planes with m catenoidal bridges between adjacent levels.
Self-shrinking Platonic solids
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abstract
We construct new embedded self-shrinkers of genus 3, 5, 7, 11 and 19 using variational methods. Our self-shrinkers resemble doublings of the Platonic solids and were discovered numerically by D. Chopp in 1994.
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Self-shrinkers with any number of ends in $\mathbb{R}^{3}$ by stacking $\mathbb{R}^{2}$
For every half-integer J and sufficiently large integer m, the authors construct an embedded self-shrinker with 2J+1 ends and genus 2J(m-1) by gluing stacked planes with m catenoidal bridges between adjacent levels.