JOURNAL OF GGT

Published in Journal of Gökova Geometry Topology, Volume 18 (2026)
Title Systolic inequality and scalar curvature
Author Shunichiro Orikasa
Abstract
We investigate the interaction between systolic geometry and positive scalar curvature through spinorial methods. Our main theorem establishes an upper bound for the two-dimensional stable systole on certain high-dimensional manifolds with positive scalar curvature under a suitable stretch-scale condition. The proof combines techniques from geometric measure theory, reminiscent of Gromov’s systolic inequality, with curvature estimates derived from the Gromov–Lawson relative index theorem. This approach provides a new framework for studying the relationship between positive scalar curvature metrics and systolic geometry in higher-dimensional manifolds.
Pages1-13
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Submitted: Feb 5, 2026
Accepted: June 7, 2026
 2026 Journal main page

Last updated: July 2026
Web address: GokovaGT.org/journal/2026