MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Currents in metric spaces
Luigi Ambrosio and Bernd KirchheimAbstract
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 by de Giorgi, is to replace the duality with differential forms by the duality with (k+1)-tuples 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 rectifiability 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 finite dimensional.
- Received:
- 08.03.00
- Published:
- 08.03.00