Local Currents in Metric Spaces |
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Authors: | Urs Lang |
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Institution: | 1.Department of Mathematics,ETH Zurich,Zurich,Switzerland |
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Abstract: | Ambrosio and Kirchheim presented a theory of currents with finite mass in complete metric spaces. We develop a variant of
the theory that does not rely on a finite mass condition, closely paralleling the classical Federer–Fleming theory. If the
underlying metric space is an open subset of a Euclidean space, we obtain a natural chain monomorphism from general metric
currents to general classical currents whose image contains the locally flat chains and which restricts to an isomorphism
for locally normal currents. We give a detailed exposition of the slicing theory for locally normal currents with respect
to locally Lipschitz maps, including the rectifiable slices theorem, and of the compactness theorem for locally integral currents
in locally compact metric spaces, assuming only standard results from analysis and measure theory. |
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