Minimal surfaces in metric spaces

度量空间中的最小曲面

• 批准号: 338892213
• 负责人: Professor Dr. Alexander Lytchak
• 金额: --
• 依托单位: Max-Planck-Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/338892213?language=en
• 关键词: Minimal; surfaces; metric; spaces

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.

在PI和第一个PI与S. Wenger的联合工作的基础上，将研究最小曲面在度量空间中的几何性质和应用。专题包括：极小圆盘在结构结果和具有上曲率边界的空间构造中的应用；极小平面在非正弯曲空间和群中的结构与应用次球面等周不等式空间中极小圆盘的结构及其在Finsler流形极小曲面和绝对填充极小化中的应用具有规定几何性质的曲面空间及其紧化和应用。