A systolic inequality with remainder in the real projective plane

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 in the real projective plane. We prove a stronger version of Pu’s systolic inequality with a remainder term.

Keywords

• systole
• geometric inequality
• riemannian submersion
• cauchy-schwarz theorem
• probabilistic variance
• 53c23
• 53a30