On a conjecture by Auerbach
type: Item
instance of: scholarly article
title: On a conjecture by Auerbach
zbMATH Open document ID: 1227.49047
DOI: 10.4171/JEMS/290
author: N. Fusco
author: Aldo Pratelli
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2011-11-14T00:00:00Z
review text: Summary: In 1938, Herman Auerbach published a paper where he showed a deep connection between the solutions of the Ulam problem of floating bodies and a class of sets studied by Zindler, which are the planar sets whose bisecting chords all have the same length. In the same paper he conjectured that among Zindler sets the one with minimal area, as well as with maximal perimeter, is the so-called ``Auerbach triangle''. We prove this conjecture.
Mathematics Subject Classification ID: 49Q10
zbMATH DE Number: 5971511
zbMATH Keywords: min-max problems
zbMATH Keywords: minimal area
zbMATH Keywords: zindler sets
zbMATH Keywords: optimal convex sets
Wikidata QID: Q123115269
MaRDI profile type: Publication
cites work: Sur un problème de M. Ulam concernant l'équilibre des corps flottants
cites work: Unsolved problems in geometry
cites work: The Maximal Length of Chords Bisecting the Area Or Perimeter Length of Plane Convex Sets
cites work: Über einige Kennzeichnungen des Kreises
cites work: Q3593480
cites work: Chords halving the area of a planar convex set
cites work: Über Zindlerkurven.
cites work: Q3236779
cites work: Q4758005
full work available at URL: https://doi.org/10.4171/jems/290
OpenAlex ID: W2082953965
description: scientific article; zbMATH DE number 5971511