Logarithmic systolic growth for hyperbolic surfaces in every genus

2024/07/02 by Mikhail G. Katz, Katz, Mikhail G., Stéphane Sabourau +1 · 1 citation
Mathematics · #53C45 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2407.02041

openalex publication_date 2024/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

More than thirty years ago, Brooks and Buser-Sarnak constructed sequences of closed hyperbolic surfaces with logarithmic systolic growth in the genus. Recently, Liu and Petri showed that such logarithmic systolic lower bound holds for every genus (not merely for genera in some infinite sequence) using random surfaces. In this article, we show a similar result through a more direct approach relying on the original Brooks/Buser-Sarnak surfaces.

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• Shortest filling geodesics on hyperbolic surfaces

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