Work

Simplex slicing: An asymptotically-sharp lower bound

Year: 2024

Type: article

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 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.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2024.109784

Author: Colin Tang

Institution: Carnegie Mellon University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,510

Funders: Carnegie Mellon University, Achievement Rewards for College Scientists Foundation