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arXiv · 2403.13224

Simplex slicing: an asymptotically-sharp lower bound

Colin Tang
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Abstract

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.

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Colin Tang. 2024-03-20. Simplex slicing: an asymptotically-sharp lower bound. https://doi.org/10.1016/j.aim.2024.109784

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