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The systole of large genus minimal surfaces in positive Ricci curvature

Henrik Matthiesen and Anna Siffert
Geometry & Topology 29 (2025) 1819–1849
DOI: 10.2140/gt.2025.29.1819
Abstract

We use Colding–Minicozzi lamination theory to show that the systole, and more generally any homology systole, of a sequence of embedded minimal surfaces in an ambient three-manifold of positive Ricci curvature tends to zero as the genus becomes unbounded.

Keywords
systole, minimal surfaces
Mathematical Subject Classification
Primary: 53A10
References
Publication
Received: 2 October 2020
Revised: 16 August 2024
Accepted: 14 September 2024
Published: 27 June 2025
Proposed: Tobias H Colding
Seconded: Gang Tian, David Fisher
Authors
Henrik Matthiesen
Max Planck Institute for Mathematics
Bonn
Germany		 Department of Mathematics
University of Chicago
Chicago, IL
United States
Anna Siffert
Mathematisches Institut
University of Münster
Münster
Germany
© 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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