# Area minimizing surfaces in homotopy classes in metric spaces

@inproceedings{Soultanis2021AreaMS, title={Area minimizing surfaces in homotopy classes in metric spaces}, author={Elefterios Soultanis and Stefan Wenger}, year={2021} }

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 Hölder 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…

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