Calculus of Variations and Geometric Measure Theory
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Decomposition of integral metric currents

Paolo Bonicatto (University of Warwick)

created by pinamonti on 14 May 2021

18 may 2021 -- 14:30   [open in google calendar]

Zoom seminar

Please write to Andrea.pinamonti@unitn.it or to Andrea.marchese@unitn.it if you want to attend the seminar.

Abstract.

Currents are nowadays a widely used tool in geometric measure theory and calculus of variations, as they allow to give a weak formulation of a variety of geometric problems. The theory of normal and integral currents (initiated mostly by Federer and Fleming in the '60s) was developed in the context of Euclidean spaces. In 2000, Ambrosio and Kirchheim introduced metric currents, defined on complete metric spaces. The talk will be devoted to integral metric currents: we show that integral currents can be decomposed as a sum of indecomposable components and, in the special case of one-dimensional integral currents, we also characterise the indecomposable ones as those associated with injective Lipschitz curves or injective Lipschitz loops. This generalises to the metric setting a previous result by Federer. Joint work with Giacomo Del Nin (Warwick) and Enrico Pasqualetto (Scuola Normale Superiore).

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