On the Gaussian Kinematic Formula of R. Adler and J. Taylor

TL;DR

This paper uses algebraic integral geometry to prove a specific case of the Gaussian kinematic formula, viewing it as a limit of spherical formulas for large-dimensional spheres.

Contribution

It provides a new proof of a special case of the Gaussian kinematic formula using algebraic integral geometry techniques.

Findings

Proves a special case of the Gaussian kinematic formula.

Shows the GKF as a limit of spherical kinematic formulas for large N.

Introduces a novel geometric approach to the GKF.

Abstract

We apply methods of algebraic integral geometry to prove a special case of the Gaussian kinematic formula of Adler-Taylor. The idea, suggested already by Adler and Taylor, is to view the GKF as the limit of spherical kinematic formulas for spheres of large dimension $N$ and curvature $\frac 1 N$.