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arXiv · 1705.09938

On some geometric properties of currents and Frobenius theorem

Giovanni Alberti·Annalisa Massaccesi
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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].

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Giovanni Alberti, Annalisa Massaccesi. 2017-12-08. On some geometric properties of currents and Frobenius theorem. https://doi.org/10.4171/rlm%2F788

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