# Asymptotic Plateau problems in spaces of higher asymptotic rank

## Urs Lang

### (ETH Zurich)

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.