A new rotational integral formula for intrinsic volumes in space forms

摘要

A new rotational version of Crofton’s formula is derived for the intrinsic volumes of a domain Y in a space form. More precisely, functional is defined on the intersection between Y and a totally geodesic submanifold (plane) through a fixed point, such that the rotational average of this functional is equal to the intrinsic volumes of Y . Particular cases of interest in stereology are considered for the Euclidean case.