Minimal Paths on Some Simple Surfaces with Singularities
Differential Geometry
2007-12-11 v6
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.
Cite
@article{arxiv.math/0401096,
title = {Minimal Paths on Some Simple Surfaces with Singularities},
author = {Joel B. Mohler and Ron Umble},
journal= {arXiv preprint arXiv:math/0401096},
year = {2007}
}
Comments
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)