Shortest closed curve to inspect a sphere

2020/10/28 by Ghomi, Mohammad, Wenk, James · 1 citation
#52A40 #58E #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Primary: 53A04 #Secondary: 52A38

paper · doi:10.48550/arxiv.2010.15204

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 4π. Equality holds only when the curve is composed of 4 semicircles of length π, arranged in the shape of a baseball seam, as conjectured by V. A. Zalgaller in 1996.

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