Simplex slicing: an asymptotically-sharp lower bound
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916296184037376 |
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| author | Tang, Colin |
| author_facet | Tang, Colin |
| contents | We show that for the regular n-simplex, the 1-codimensional central slice that's parallel to a facet will achieve the minimum area (up to a 1-o(1) factor) among all 1-codimensional central slices, thus improving the previous best known lower bound (Brzezinski 2013) by a factor of $\frac{2\sqrt{3}}{e} \approx 1.27$. In addition to the standard technique of interpreting geometric problems as problems about probability distributions and standard Fourier-analytic techniques, we rely on a new idea, mainly \emph{changing the contour of integration} of a meromorphic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simplex slicing: an asymptotically-sharp lower bound Tang, Colin Metric Geometry Functional Analysis We show that for the regular n-simplex, the 1-codimensional central slice that's parallel to a facet will achieve the minimum area (up to a 1-o(1) factor) among all 1-codimensional central slices, thus improving the previous best known lower bound (Brzezinski 2013) by a factor of $\frac{2\sqrt{3}}{e} \approx 1.27$. In addition to the standard technique of interpreting geometric problems as problems about probability distributions and standard Fourier-analytic techniques, we rely on a new idea, mainly \emph{changing the contour of integration} of a meromorphic function. |
| title | Simplex slicing: an asymptotically-sharp lower bound |
| topic | Metric Geometry Functional Analysis |
| url | https://arxiv.org/abs/2403.13224 |