The extremal length systole of the Bolza surface

TL;DR

This paper proves that the Bolza surface, a genus two surface, uniquely maximizes the extremal length systole locally, with the maximum value being A2.

Contribution

It establishes the extremal length systole's strict local maximum at the Bolza surface, highlighting its special geometric extremality among genus two surfaces.

Findings

Bolza surface attains a local maximum of extremal length systole

Maximum value of the systole at Bolza surface is A2

The result emphasizes the geometric extremality of the Bolza surface

Abstract

We prove that the extremal length systole of genus two surfaces attains a strict local maximum at the Bolza surface, where it takes the value $\sqrt{2}$.