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Bibliographic Details
Main Author: Tabachnikov, Serge
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.12609
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author Tabachnikov, Serge
author_facet Tabachnikov, Serge
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_12609
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A 4-point theorem: still another variation on an old theme
Tabachnikov, Serge
Differential Geometry
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.
title A 4-point theorem: still another variation on an old theme
topic Differential Geometry
url https://arxiv.org/abs/2409.12609