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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2025 Volume 216, Number 9, Pages 21–41 (Mi sm10158)

The coarea formula for projections of Lipschitz maps of Carnot groups

S. G. Basalaev

Faculty of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia

Abstract: A special coarea inequality is established for the compositions of Lipschitz maps of Carnot groups with projections along horizontal vector fields. Equality is proved for maps with finite codistortion and maps acting on the Heisenberg group.
Bibliography: 42 titles.

Keywords: Carnot group, coarea formula, Eilenberg's inequality.

MSC: Primary 22E30, 28A75, 28A78; Secondary 58C35

Received: 10.07.2024 and 20.09.2024

DOI: 10.4213/sm10158


 English version:
Sbornik: Mathematics, 2025, 216:9, 1211–1230

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© Steklov Math. Inst. of RAS, 2026