On sphere-filling ropes

Abstract

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing patterns in chemistry, or to ordered phases of long elastic rods stuffed into spherical shells.

15 pages, 8 figures

References in corpus (1)

• Self-contact Sets for 50 Tightly Knotted and Linked Tubes

Cited by in corpus (3)

• Tangent-point self-avoidance energies for curves
• Characterizing $W^{2,p}$~submanifolds by $p$-integrability of global curvatures
• Sobolev Gradients for the Möbius Energy