Hyperplane Sections of Cylinders

TL;DR

This paper derives a formula for the volume of hyperplane sections of cylinders, proves an integral inequality involving Bessel functions, and determines maximal sections for large cylinders.

Contribution

It introduces a new formula for cylinder hyperplane sections and establishes an inequality that bounds their volumes, advancing geometric analysis techniques.

Findings

Derived a volume formula for cylinder hyperplane sections

Proved an integral inequality involving Bessel functions

Identified maximal sections for large cylinders

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.