Institute for Mathematical Physics Currents in Metric Spaces Currents in Metric Spaces
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.
منابع مشابه
On metric spaces induced by fuzzy metric spaces
For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm, we present a method to construct a metric on a fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space. Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...
متن کاملA common fixed point theorem on ordered metric spaces
A common fixed point result for weakly increasing mappings satisfying generalized contractive type of Zhang in ordered metric spaces are derived.
متن کاملOn the Structure of Metric-like Spaces
The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...
متن کاملFixed point results in cone metric spaces endowed with a graph
In this paper, we prove the existence of fixed point for Chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. The main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.
متن کامل