A kinematic formula for the total absolute curvature

TL;DR

This paper extends classical kinematic formulas to include total absolute curvature for compact PL-subspaces in Euclidean space, providing a new integral geometric relation.

Contribution

It introduces a kinematic formula for total absolute curvature applicable to compact PL-subspaces, generalizing classical results.

Findings

Established a kinematic formula for total absolute curvature.

Demonstrated the analogy to classical kinematic formulas.

Applicable to compact PL-subspaces in Euclidean space.

Abstract

Let $A$ and $B$ be compact PL-subspaces of some euclidean space $E^n$. We show that for these a kinematic formula for the total absolute curvature holds in analogy to the classical one.