Hyperplane sections of cylinders
Volume 147 / 2017
Colloquium Mathematicum 147 (2017), 145-164
MSC: Primary 52A40; Secondary 52A20, 52A38, 33C10.
DOI: 10.4064/cm6909-5-2016
Published online: 9 December 2016
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 radii of the cylinder we determine the maximal section.
