Self-shrinking Platonic solids

2016/02/23 by Daniel Ketover, Ketover, Daniel · 5 citations
Mathematics · #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1602.07271

arxiv created 2016/02/23 · arxiv updated 2016/02/24

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.

Cited by

• Closed mean curvature flows with prescribed tangent flows
• Mean curvature flow with generic initial data
• Self-shrinkers with any number of ends in ℝ³ by stacking ℝ²
• On the topological rigidity of self shrinkers in ℝ³
• Asymptotic structure of self-shrinkers

Related

• Immersed self-shrinkers
• Closed self-shrinking surfaces in ℝ³ via the torus
• Self-shrinkers with any number of ends in ℝ³ by stacking ℝ²
• Self-shrinkers whose asymptotic cones fatten
• Embedded self-similar shrinkers of genus 0