# 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