The Coarea Formula for Vector Functions on Carnot Groups with Sub-Lorentzian Structure

Abstract

We establish the coarea formula as an expression for the measure of a subset of a Carnot group in terms of the sub-Lorentzian measure of the intersections of the subset with the level sets of a vector function. We describe the conditions for the level sets of vector functions to be spacelike and find the metric characteristics of these surfaces. Also, we address a series of relevant questions, in particular, about the uniqueness of the coarea factor.