Minimal surfaces in metric spaces

在最近两个PI的工作以及第一个PI与S.Wenger的联合工作的基础上，我们将研究度量空间中极小曲面的几何性质和应用。特别主题包括：极小圆盘在结构结果和具有曲率上界的空间的构造中的应用；极小平面在非正弯曲空间和群中的结构和应用；具有次球面等周不等长的空间中极小圆盘的结构和应用；Finsler流形中的极小曲面和绝对填充极小元；具有指定几何性质的曲面空间，它们的紧致化和应用。

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.