Extremal sections and projections of certain convex bodies: a survey
Piotr Nayar, Tomasz Tkocz
Abstract
We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly ℓp-balls, by and onto lower-dimensional subspaces. This subject emerged from geometry of numbers several decades ago and since then has seen the development of a variety of probabilistic and analytic methods, showcased in this chapter.
Topics & Concepts
Linear subspaceRegular polygonVariety (cybernetics)Probabilistic logicMathematicsSubject (documents)GeometryCombinatoricsComputer scienceStatisticsLibrary sciencePoint processes and geometric inequalities