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Hyperplane sections of cylinders

Volume 147 / 2017

Hauke Dirksen Colloquium Mathematicum 147 (2017), 145-164 MSC: Primary 52A40; Secondary 52A20, 52A38, 33C10. DOI: 10.4064/cm6909-5-2016 Published online: 9 December 2016


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 radii of the cylinder we determine the maximal section.


  • Hauke DirksenDepartment of Mathematics
    Kiel University
    24118 Kiel, Germany

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