  We introduce and study a notion of relative 1-homotopy type for Sobolev maps
from a surface to a metric space spanning a given collection of Jordan curves.
We use this to establish the existence and local H\"older regularity of area
minimizing surfaces in a given relative 1-homotopy class in proper geodesic
metric spaces admitting a local quadratic isoperimetric inequality. If the
underlying space has trivial second homotopy group then relatively 1-homotopic
maps are relatively homotopic. We also obtain an analog for closed surfaces in
a given 1-homotopy class. Our theorems generalize and strengthen results of
Lemaire, Jost, Schoen-Yau, and Sacks-Uhlenbeck.
