Flat convergence for integral currents in metric spaces |
| |
Authors: | Stefan Wenger |
| |
Institution: | (1) Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012-1185, USA |
| |
Abstract: | In compact local Lipschitz neighborhood retracts in
weak convergence for integral currents is equivalent to convergence with respect to the flat distance. This comes as a consequence of the deformation theorem for currents in Euclidean space. Working in the setting of metric integral currents (the theory of which was developed by Ambrosio and Kirchheim) we prove that the equivalence of weak and flat convergence remains true in the more general context of metric spaces admitting local cone type inequalities. These include in particular all Banach spaces and all CAT(κ)-spaces. As an application we obtain the existence of a minimal element in a fixed homology class and show that the weak limit of a sequence of minimizers is itself a minimizer. |
| |
Keywords: | Integral currents Flat distance Weak convergence Alexandrov spaces |
本文献已被 SpringerLink 等数据库收录! |