A Systolic Inequality for the Filling Area Conjecture

2023/01/20 by Chaitanya Ambi, Ambi, Chaitanya
Mathematics · #Point processes and geometric inequalities #Geometric and Algebraic Topology #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2301.08503

Abstract

We prove an upper bound on the systolic ratio of an orientable isometric filling of the circle equipped with a Riemannian metric. The bound depends only on the genus of isometric filling. We also apply the bound to the class of orientable isometric filling with a certain lower bound on the systole. We deduce that the Filling Area Conjecture holds true for this class when the genus is sufficiently large.

Related

• Systolic inequalities for metric surfaces via filling minimality
• Filling area conjecture, optimal systolic inequalities, and the fiber class in abelian covers
• Stability of systolic inequalities for the Möbius strip and Klein bottle
• A local systolic inequality and Gromov's filling area conjecture
• Construction of surfaces with large systolic ratio