An isoperimetric inequality for logarithmic capacity of polygons

Pages 277-303 from Volume 159 (2004), Issue 1 by Alexander Yu. Solynin, Victor A. Zalgaller

Abstract

We verify an old conjecture of G. Pólya and G. Szegő saying that the regular $n$-gon minimizes the logarithmic capacity among all $n$-gons with a fixed area.

Mathematical Subject Classification

Primary 2000: Secondary:

DOI
https://doi.org/10.4007/annals.2004.159.277
MR
2052355
zbMATH
1060.31001
Milestones
Received: 25 May 2001
Revised: 17 June 2002
Accepted: 20 May 2002
Published online: January 2004

Authors

Alexander Yu. Solynin

Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, United States

Victor A. Zalgaller

Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel