| 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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