Minimal surfaces in metric spaces

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Building on recent work of both PIs and joint work of the first PI with S. Wenger, the geometric properties and applications of minimal surfaces in metric spaces will be investigated. Special topics include: Applications of minimal discs to structural results and constructions of spaces with upper curvature bounds; structure and applications of minimal planes to non-positively curved spaces and groups; structure of minimal discs in spaces with sub-spherical isoperimetric inequality and applications to minimal surfaces in Finsler manifolds and to absolute filling minimizers; spaces of surfaces with prescribed geometric properties, their compactifications and applications.