10 Dez 2014
16:00  - 16:45

Rheinsprung 21, Grosser Hörsaal

Seminar Analysis: Annalisa Massaccesi (University of Zurich)

Frobenius property for integral currents and decomposition of normal currents

 

In this joint work with Giovanni Alberti, we prove a Frobenius property for inte-gral currents: namely, if R=[∑,ξ,θ] k-dimensional integral current with a simple tangent vector field ξ∈C1(Rdk(Rd)), then ξ is involtive at almost every point in ∑. This result is related to the following decomposition problem formulated by F.Morgan: given a k-dimensional normal current T, do there exist a measure space L and a family of rectifiable currents {Rλ}λ∈L such that T = ∫L Rλ dλ and the mass decomposes consistently as M(T) = ∫L M(Rλ) dλ? The aforementioned Frobenius property allows us to provide a counterexample to the existence of such a decomposition with a family of integral currents.


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