Area minimizing surfaces of bounded genus in metric spaces

Abstract The Plateau–Douglas problem asks to find an area minimizing surface of fixed or bounded genus spanning a given finite collection Jordan curves in Euclidean space. In the present paper we solve this setting proper metric spaces admitting local quadratic isoperimetric inequality for curves. We moreover obtain continuity up boundary and interior Hölder regularity solutions. Our results generalize corresponding Jost Tomi-Tromba from Riemannian manifolds that with inequality. special case disc-type single curve corresponds classical Plateau, recently solved by Lytchak second author.