A systolic inequality with remainder in the real projective plane

TL;DR

This paper improves Pu's classical systolic inequality for the real projective plane by establishing a stronger version that includes a remainder term, advancing understanding in systolic geometry.

Contribution

It introduces a refined systolic inequality with a remainder term for the real projective plane, strengthening the classical result by Pu.

Findings

Established a stronger systolic inequality with a remainder term

Enhanced the understanding of metric properties on the real projective plane

Contributed to the development of systolic geometry theory

Abstract

The first paper in systolic geometry was published by Loewner's student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric on the real projective plane. We prove a stronger version of Pu's systolic inequality with a remainder term.