Coarea Formula for Functions on 2-Step Carnot Groups with Sub-Lorentzian Structure

M. B. Karmanova

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia

Correspondence to: e-mail: maryka@math.nsc.ru

Received 2 December, 2019

Abstract—We consider C¹-functions defined on two-step Carnot groups with a sub-Lorentzian structure defined by one horizontal direction with a negative squared length along it, and prove a nonholonomic coarea formula. A result of interest in itself concerns the correctness of the problem statement, namely, the level sets have to be spacelike.

Keywords: two-step Carnot group, sub-Lorentzian structure, level set, sub-Lorentzian measure, coarea formula

DOI: 10.1134/S1064562420020131