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.
Angenent, Shrinking doughnuts, Nonlinear diffusion equations and their equilibrium states, 3 (Greg- ynog, 1989)
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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.