CRM: Centro De Giorgi
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ERC School on Analysis in Metric Spaces and Geometric Measure Theory

Rectifiable and Flat Chains and Charges in a Metric Space

speaker: Robert Hardt (Mathematics Department, Rice University, Houston TX, USA)

abstract: Rectifiability and compactness properties for Euclidean-space chains having coefficients in a finite group G were studied by W. Fleming(1966). This allowed for the modeling of unorientable least-area surfaces including a minimal Mobius band in 3-space. These properties were optimally extended by Brian White (1999) to any complete normed abelian group which contains no nonconstant Lipschitz curves. Independently L.Ambrosio and B.Kirchheim (2000) also generalized some basic rectifiability theorems of Federer and Fleming to the new notion of currents in a general metric space. Our recent work with T. De Pauw shares features and results with all these works, includes new definitions of a flat G chains in a metric space, and a proof that such a chain is determined by its 0 dimensional slices. Some classes of such chains give homology theories. Related dual cohomology theories involve the charges, introduced by De Paul, Moonens, and Pfeffer, which are dual to normal currents, suitably topologized. We will review all these works.

Mon 10 Jan, 9:00 - 9:50, Aula Dini
Mon 10 Jan, 16:00 - 16:50, Aula Dini
Tue 11 Jan, 14:30 - 15:20, Aula Dini
Wed 12 Jan, 10:00 - 10:50, Aula Dini
Fri 14 Jan, 9:00 - 9:50, Aula Dini
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