Systolic Inequality and Scalar Curvature

Shunichiro Orikasa

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arXiv · 2509.17376

Systolic Inequality and Scalar Curvature

Shunichiro Orikasa

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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.

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Shunichiro Orikasa. 2025-09-22. Systolic Inequality and Scalar Curvature. https://arxiv.org/abs/2509.17376

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