On the four-vertex theorem
type: Item
instance of: scholarly article
title: On the four-vertex theorem
zbMATH Open document ID: 0635.53003
DOI: 10.1007/BF01830673
author: Ulrich Pinkall
published in: Aequationes Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137241
review text: A four-vertex theorem for closed plane curves with possible self- intersections is proved. The curves have to satisfy the additional condition that they bound a surface which is immersed into the plane. The proof uses methods from conformal differential geometry. A higher-vertex theorem is conjectured for the case of surfaces of higher genus.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53A30
zbMATH DE Number: 4034543
zbMATH Keywords: four-vertex theorem
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: Zur Möbius-Geometrie: Die Inversionsgeometrie ebener Kurven.
cites work: Spherical Curves that Bound Immersed Discs
cites work: Extensions of the Four-Vertex Theorem
cites work: Zur Verallgemeinerung des Vierscheitelsatzes und seiner Umkehrung
cites work: Streng-konvexe Bogen und Kurven in der direkten Infinitesimalgeometrie
cites work: Planar surface immersions
cites work: Immersions and \opertornameMod-2 Quadratic Forms
cites work: Q4119824
cites work: Extended minimum-number theorems of cyclic and sextactic points on a plane convex oval
cites work: The Four-or-More Vertex Theorem
cites work: Vierscheitelsatz auf Flächen nichtpositiver Krümmung
cites work: Q3242583
description: scientific article; zbMATH DE number 4034543