On some geometric properties of currents and Frobenius theorem

  • Giovanni Alberti

    Università di Pisa, Italy
  • Annalisa Massaccesi

    Universität Zürich, Switzerland

Abstract

In this note we announce some results, due to appear in [2], [3], on the structure of integral and normal currents, and their relation to Frobenius theorem. In particular we show that an integral current cannot be tangent to a distribution of planes which is nowhere involutive (Theorem 3.6), and that a normal current which is tangent to an involutive distribution of planes can be locally foliated in terms of integral currents (Theorem 4.3). This statement gives a partial answer to a question raised by Frank Morgan in [1].

Cite this article

Giovanni Alberti, Annalisa Massaccesi, On some geometric properties of currents and Frobenius theorem. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 4, pp. 861–869

DOI 10.4171/RLM/788