Simplex slicing: An asymptotically-sharp lower bound
Colin Tang · Advances in Mathematics · 2024
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 2 3 e ≈ 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 changing the contour of integration of a meromorphic function.