论文标题
面积最小
Area minimizing surfaces in homotopy classes in metric spaces
论文作者
论文摘要
我们介绍并研究了Sobolev地图的相对1-HOMOTOPY类型的概念，从表面到度量空间，涵盖了给定的Jordan曲线集合。我们用它来确定在适当的地球仪式空间中给定相对1-摩托验证类别中最小化表面的面积的存在和局部霍尔德规律性，并承认局部二次等法不平等现象。如果基础空间具有微不足道的第二均同喻组，则相对1-托管图相对均匀。我们还获得了给定的1-HOMOTOPY类中闭合表面的类似物。我们的定理概括并加强了Lemaire，Jost，Schoen-Yau和Sacks-Uhlenbeck的结果。
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 obtain an analog for closed surfaces in a given 1-homotopy class. Our theorems generalize and strengthen results of Lemaire, Jost, Schoen-Yau, and Sacks-Uhlenbeck.
