论文标题
在共形锥中最小化问题的区域，ii
The area minimizing problem in conformal cones, II
论文作者
论文摘要
在本文中，我们继续研究该区域之间的联系，最小化问题，某些区域功能和最小表面方程的差异问题，在一类共形锥中，具有类似的动机\ cite {gz20}。这些锥体是双曲线空间的某些概括。我们描述了最小化$ n $ nteger多重电流的区域的结构，其中$ c^2 $共形锥带有规定的$ c^1 $图形边界，通过这些区域功能的最小问题。作为一种应用，我们解决了平均凸型假设下最小表面方程的相应差异问题。我们还将其最小化的整数多重电流延伸到双曲线空间中的星形无穷大边界的局部区域的存在和唯一性中，到一大批完整的保形歧管中。
In this paper we continue to study the connection among the area minimizing problem, certain area functional and the Dirichlet problem of minimal surface equations in a class of conformal cones with a similar motivation from \cite{GZ20}. These cones are certain generalizations of hyperbolic spaces. We describe the structure of area minimizing $n$-nteger multiplicity currents in bounded $C^2$ conformal cones with prescribed $C^1$ graphical boundary via a minimizing problem of these area functionals. As an application we solve the corresponding Dirichlet problem of minimal surface equations under a mean convex type assumption. We also extend the existence and uniqueness of a local area minimizing integer multiplicity current with star-shaped infinity boundary in hyperbolic spaces into a large class of complete conformal manifolds.
