A 4-point theorem: still another variation on an old theme
Differential Geometry
2024-09-20 v1
Abstract
An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend this result to the spherical and hyperbolic geometries - in the latter case, to horocyclically convex curves only.
Keywords
Cite
@article{arxiv.2409.12609,
title = {A 4-point theorem: still another variation on an old theme},
author = {Serge Tabachnikov},
journal= {arXiv preprint arXiv:2409.12609},
year = {2024}
}