Noncontact mappings of general Carnot groups and a coarea formula

M. B. Karmanova<sup>ab

a</sup> Novosibirsk State University, Novosibirsk, Russia
^b Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: A coarea formula is established for mappings of Carnot groups of arbitrary depth. One of the key properties is the description of the relationship between Hausdorff measures constructed using sub-Riemannian and Riemannian quasimetric structures.

Keywords: Carnot group, level set, Hausdorff dimension, coarea formula.

UDC: 517.518.1

MSC: 35R30

Received: 01.08.2024
Revised: 01.08.2024
Accepted: 25.06.2025

DOI: 10.33048/smzh.2025.66.408

 English version: Siberian Mathematical Journal, 2025, 66:4, 952–973