The Longest Shortest Fence and Sharp Poincaré–Sobolev Inequalities

被引：0
|
作者：
L. Esposito
V. Ferone
B. Kawohl
C. Nitsch
C. Trombetti
机构：
[1] Universitá di Salerno,Dipartimento di Matematica e Informatica
[2] Universitá di Napoli Federico II,Dipartimento di Matematica e Applicazioni “R. Caccioppoli”
[3] Complesso Universitario Monte S. Angelo,Mathematisches Institut
[4] Universität zu Köln,undefined
来源：
Archive for Rational Mechanics and Analysis | 2012年 / 206卷
关键词：
Equilateral Triangle; Sobolev Inequality; Isosceles Triangle; Terminal Point; Straight Segment;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：821 / 851
页数：30
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