Primitives of volume forms in Carnot groups

  • Annalisa Baldi

    University of Bologna, Italy
  • Bruno Franchi

    University of Bologna, Italy
  • Pierre Pansu

    Université Paris-Saclay, CNRS, Orsay, France
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Abstract

In the Euclidean space, it is known that a function of a ball, with vanishing average, is the divergence of a vector field with . In this note, we prove a similar result in any Carnot group for a vanishing average , , where is the so-called homogeneous dimension of .

Cite this article

Annalisa Baldi, Bruno Franchi, Pierre Pansu, Primitives of volume forms in Carnot groups. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 35 (2024), no. 4, pp. 597–617

DOI 10.4171/RLM/1052