Systolic Inequality and Scalar Curvature
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914060623151104 |
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| author | Orikasa, Shunichiro |
| author_facet | Orikasa, Shunichiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Systolic Inequality and Scalar Curvature Orikasa, Shunichiro Differential Geometry 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. |
| title | Systolic Inequality and Scalar Curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.17376 |