Conformal Geometric Inequalities on the Klein Bottle

TL;DR

This paper establishes three optimal conformal geometric inequalities on the Klein bottle, providing bounds on volume and curve lengths related to systolic geometry.

Contribution

It introduces new conformal inequalities specific to the Klein bottle, advancing the understanding of systolic geometry in this non-orientable surface.

Findings

Proved three optimal inequalities of Blatter type on the Klein bottle.

Established conformal lower bounds for volume and systolic curve lengths.

Identified candidate curves that realize the systole on the Klein bottle.

Abstract

We prove three optimal conformal geometric inequalities of Blatter type on the Klein bottle. These inequalities provide conformal lower bounds of the volume and involve lengths of homotopy classes of curves that are candidates to realize the systole.