An isoperimetric inequality for logarithmic capacity of polygons

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.

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