On the extension of Frobenius theorem to non-smooth sets and currents
speaker: Giovanni Alberti (Dipartimento di Matematica, Università di Pisa)abstract: Given a distribution V of k-planes in Rd, on of the implications in the classical version of Frobenius theorem can be stated as follows: if S is a regular k-dimensional surface tangent to V , then V is involutive at every point of S. In this talk I will give an overview of some recent (and not so recent) research with A. Massaccesi (University of Verona), Evgeni Stepanov (Steklov Institute, Saint Petersburg) and Andrea Merlo (Scuola Normale Superiore, Pisa), where we investigated the extension of this statement to weaker notions of surfaces, such as recti fiable sets and currents. In particular, if S is a just a (k-rectifi able) set and not a regular surface, then the validity of the statement is strictly related to the regularity of the boundary of S. Furthermore, if S is normal current, then the key is a certain geometric property of the boundary of S. It should be noted that these questions are strictly related to the problem of decomposing normal currents into integral currents.
timetable:
Thu 17 Jan, 9:30 - 10:30, Aula Magna Bruno Pontecorvo
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