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A bound on the number of endpoints of the cut locus. (English) Zbl 1111.53004

Summary: The authors provide strong experimental evidence for an upper bound on the number of endpoints of the cut locus from a point on a 2-surface of revolution. This bound is equal to the minimal number of intervals of monotone non-increasing or non-decreasing Gaussian curvature along one meridian from one pole to the other.

MSC:

53A05 Surfaces in Euclidean and related spaces
53-04 Software, source code, etc. for problems pertaining to differential geometry
53C22 Geodesics in global differential geometry
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

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