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Rectifiable and Flat G-Chains in a Metric Space

Mercoledi' 2 marzo 2011 - Robert Hardt

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Mercoledi' 2 marzo alle ore 12:15 in aula 1BC45 Robert Hardt (Rice University, Houston) terra' un seminario dal titolo "Rectifiable and Flat G-Chains in a Metric Space".

-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. The new proofs of basic theorems from Geometric Measure Theory involved slicing to reduce to questions about 0 dimensional chains (which are finite or countable sums of weighted point masses). Independently L.Ambrosio and B.Kirchheim (2000) also generalized some basic rectifiability theorems of Federer and Fleming to currents in a general metric space. Our current 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.

Rif. int. M. Bardi, C. Marchi, M. Novaga

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