Shortest closed curve to inspect a sphere
Differential Geometry
2021-07-23 v2 Metric Geometry
Abstract
We show that in Euclidean 3-space any closed curve which lies outside the unit sphere and contains the sphere within its convex hull has length at least . Equality holds only when the curve is composed of semicircles of length , arranged in the shape of a baseball seam, as conjectured by V. A. Zalgaller in 1996.
Cite
@article{arxiv.2010.15204,
title = {Shortest closed curve to inspect a sphere},
author = {Mohammad Ghomi and James Wenk},
journal= {arXiv preprint arXiv:2010.15204},
year = {2021}
}
Comments
25 pages, 9 figures; The proof has been simplified and shortened; Accepted for publication in J. Reine Angew. Math. (Crelle's Journal)