Hyperplane sections of cylinders

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2017Embargo end date: 01 Jan 2016 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Colloquium Mathematicum, volume 147, pages 145-164 (issn: 0010-1354, eissn: 1730-6302,

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Authors: Dirksen, Hauke;

doi: 10.4064/cm6909-5-2016 , 10.48550/arxiv.1602.07854

arXiv: 1602.07854

Hyperplane sections of cylinders

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Abstract

We provide a formula to compute the volume of the intersection of a generalized cylinder with a hyperplane. Then we prove an integral inequality involving Bessel functions similar to Keith Ball's well-known inequality. Using this inequality we obtain upper bounds for the section volume. For large radius of the cylinder we determine the maximal section.

Related Organizations

Kiel University
Germany

Keywords

Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG), Primary 52A40, Secondary 52A20, 52A38, 33C10

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