Universität zu Köln

Esposito, L., Ferone, V., Kawohl, B., Nitsch, C. and Trombetti, C. (2012). The Longest Shortest Fence and Sharp Poincare-Sobolev Inequalities. Arch. Ration. Mech. Anal., 206 (3). S. 821 - 852. NEW YORK: SPRINGER. ISSN 0003-9527

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Abstract

We prove a long standing conjecture concerning the fencing problem in the plane: among planar convex sets of given area, the disc, and only the disc, maximizes the length of the shortest area-bisecting curve. Although it may look intuitive, the result is by no means trivial since we also prove that among planar convex sets of given area the set which maximizes the length of the shortest bisecting chords is the so-called Auerbach triangle.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Esposito, L. UNSPECIFIED UNSPECIFIED UNSPECIFIED Ferone, V. UNSPECIFIED UNSPECIFIED UNSPECIFIED Kawohl, B. UNSPECIFIED UNSPECIFIED UNSPECIFIED Nitsch, C. UNSPECIFIED UNSPECIFIED UNSPECIFIED Trombetti, C. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-478295
DOI:	10.1007/s00205-012-0545-0
Journal or Publication Title:	Arch. Ration. Mech. Anal.
Volume:	206
Number:	3
Page Range:	S. 821 - 852
Date:	2012
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	0003-9527
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics, Applied; Mechanics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47829