Minimal Paths on Some Simple Surfaces with Singularities

2004/01/09 by Joel B. Mohler, Mohler, Joel B., Ron Umble +1
Computer Science · Mathematics · #53A04 #53A05 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #math.DG #msc:53A04 #msc:53A05

paper · pdf · doi:10.48550/arxiv.math/0401096

12 pages, 7 figures (v6:typo fixes in Lemma 1) (v5:revised the Ascoli argument in the first paragraph) (v4:Editorial revisions pursuant to referee's report) (v3:Revision of Title from "Minimal Paths on Unicone and Bicylinder Boundaries"; Other editorial revisions)

openalex publication_date 2004/01/09 · arxiv created 2007/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given two points on a soup can or conical cup with lid, we find and classify all paths of minimal length connecting them. When the number of minimal paths is finite, there are at most four on a can and three on a cup. At worst, minimal paths are piece-wise smooth with three components, each of which is a classical geodesic. Minimal paths are geodesics in the sense of Banchoff.

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