On some geometric properties of currents and Frobenius theorem

Giovanni Alberti, Annalisa Massaccesi
2017 Rendiconti Lincei - Matematica e Applicazioni  
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
more » ... er to a question raised by Frank Morgan in [1].
doi:10.4171/rlm/788 fatcat:5ajzrktdxjaj3edyslt74yd3uu