Triangles on planar Jordan $C^1$-curves
Metric Geometry
2013-02-27 v2
Abstract
We prove that a Jordan -curve in the plane contains any non-flat triangle up to translation and homothety with positive ratio. This is false if the curve is not . The proof uses a bit configuration spaces, differential and algebraic topology as well as the Schoenflies theorem. A partial generalization holds true in higher dimensions.
Keywords
Cite
@article{arxiv.1205.0231,
title = {Triangles on planar Jordan $C^1$-curves},
author = {Jean-Claude Hausmann},
journal= {arXiv preprint arXiv:1205.0231},
year = {2013}
}
Comments
13 pages, 2 fugures. A new section (Section 5) has been added containing a partial generalization of the main theorem in higher dimensions