ESI The Erwin Schr odinger
نویسندگان
چکیده
We develop a theory of currents in metric spaces which extends the classical theory of Federer{Fleming in euclidean spaces and in Riemannian manifolds. The main idea, suggested in 20, 21], is to replace the duality with diierential forms with the duality with (k + 1)-ples (f; 1; : : : ; k) of Lipschitz functions, where k is the dimension of the current. We show, by a metric proof which is new even for currents in euclidean spaces, that the closure theorem and the boundary rectiiability theorem for integral currents hold in any complete metric space E. Moreover, we prove some existence results for a generalized Plateau problem in compact metric spaces and in some classes of Banach spaces, not necessarily nite dimensional.
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ESI The Erwin Schr odinger
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