The Longest Shortest Fence and Sharp Poincare-Sobolev Inequalities

被引：27

作者：

Esposito, L. ^{[1
]}

Ferone, V. ^{[2
]}

Kawohl, B. ^{[3
]}

Nitsch, C. ^{[2
]}

Trombetti, C. ^{[2
]}

机构：

[1] Univ Salerno, Dipartimento Matemat & Informat, I-84084 Fisciano, SA, Italy

[2] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

[3] Univ Cologne, Math Inst, D-50923 Cologne, Germany

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2012年 / 206卷 / 03期

关键词：

Equilateral Triangle; Sobolev Inequality; Isosceles Triangle; Terminal Point; Straight Segment;

D O I：

10.1007/s00205-012-0545-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：821 / 851

页数：31

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