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Extremal sections and projections of certain convex bodies: a survey

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arxiv 2210.00885 v3 pith:CYIJ7LCC submitted 2022-10-03 math.FA math.MGmath.PR

Piotr Nayar , Tomasz Tkocz This is my paper · ORCID
classification math.FAmath.MGmath.PR
keywords surveybodiescertainconvexprojectionssectionsanalyticballs
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abstract

We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly $\ell_p$ balls, by and onto lower dimensional subspaces. This subject emerged from geometry of numbers several decades ago and since then has seen development of a variety of probabilistic and analytic methods, showcased in this survey.

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  1. On the Number of Vertices in a Hyperplane Section of a Polytope

    math.CO 2024-12 conditional novelty 6.0 of 10

    The cyclic polytope attains the maximum number of vertices in a hyperplane slice, and the paper determines the missing vertex counts, or gaps, for slices of hypercubes up to dimension seven.

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