Asymptotic Plateau problems in spaces of higher asymptotic rank

Urs Lang

(ETH Zurich)

Event: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Date: Oct 12, 2011, time: 10:40

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. (Joint work with Bruce Kleiner.) We study \(n\)-dimensional (quasi-)minimizing varieties (locally integral currents) in nonpositively curved metric spaces of rank \(n\) in an asymptotic sense. The varieties considered have polynomial volume growth of order \(n\). We prove several results regarding the existence, stability, persistence under deformations of the metric, and the asymptotic geometry of such (quasi-)minimizers. Some of these are parallel to known results on quasi-geodesics or higher-dimensional quasi-minimizers in hyperbolic spaces.