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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.20129 |
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| _version_ | 1866929366332604416 |
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| author | Chow, Tsz-Kiu Aaron Zhu, Jingze |
| author_facet | Chow, Tsz-Kiu Aaron Zhu, Jingze |
| contents | This paper investigates quantitative metric inequalities for manifolds with positive isotropic curvature (PIC). Our results include upper bounds on the bandwidth and focal radius of hypersurfaces in PIC manifolds, contingent on boundary convexities and Betti numbers. The proof is based on exploiting the spectral properties of a twisted de Rham-Hodge operator on manifolds with boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bandwidth and focal radius with positive isotropic curvature Chow, Tsz-Kiu Aaron Zhu, Jingze Differential Geometry Geometric Topology This paper investigates quantitative metric inequalities for manifolds with positive isotropic curvature (PIC). Our results include upper bounds on the bandwidth and focal radius of hypersurfaces in PIC manifolds, contingent on boundary convexities and Betti numbers. The proof is based on exploiting the spectral properties of a twisted de Rham-Hodge operator on manifolds with boundary. |
| title | Bandwidth and focal radius with positive isotropic curvature |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2405.20129 |