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Self-shrinking Platonic solids

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arxiv 1602.07271 v1 pith:XLVLLIPB submitted 2016-02-23 math.DG math.AP

Daniel Ketover This is my paper · ORCID
classification math.DGmath.AP
keywords platonicself-shrinkerssolidschoppconstructdiscovereddoublingsembedded
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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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  1. Self-shrinkers with any number of ends in $\mathbb{R}^{3}$ by stacking $\mathbb{R}^{2}$

    math.DG 2025-07 conditional novelty 7.0 of 10

    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.

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