论文标题
部分自由边界最小的半磁盘的空间
The space of partially free boundary minimal half disks
论文作者
论文摘要
本文构成了我们正在进行的作品的一部分，该作品是在具有边界的渐近平坦的三维Riemannian歧管中存在完全非紧密的自由边界最小平面。我们为三维半球中正确嵌入的部分自由边界最小半磁盘的空间设置了学位理论。我们证明了这种表面的空间是Banach的歧管。投影映射部分将部分自由边界最小的半磁盘投射到其dirichlet边界中是索引零的弗雷德·霍尔姆图，并且在适当的假设下具有明确定义的mod-2度。新的主要分析困难是分析具有弯道域上具有混合边界条件的二阶椭圆算子的性质。
This paper forms part of our ongoing works on the existence of complete non-compact free boundary minimal planes in an asymptotically flat three-dimensional Riemannian manifold with boundary. We set up the degree theory for the space of properly embedded partially free boundary minimal half disks in a three-dimensional half ball. We prove that the space of such surfaces is a Banach manifold. The projection map which projects partially free boundary minimal half disks into their Dirichlet boundaries is a Fredholm map of index zero and has a well-defined mod-2 degree under suitable assumptions. The new major analytic difficulty is to analyze the properties of a second order elliptic operator with mix boundary conditions on a domain with corners.
