The area minimizing problem in conformal cones, II
The area minimizing problem in conformal cones, II
复制标题
共角锥体的面积最小化问题，II
DOI：
10.1007/s11425-020-1792-3
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Hengyu Zhou
中科院分区：
文献类型：
--
作者：
Qiang Gao;Hengyu Zhou
本文继续研究一类共形锥中极小曲面方程的面积极小化问题、面积泛函与Dirichlet问题之间的联系，其动机与文献[15]类似。这些锥是双曲空间的某些推广。我们描述的结构，面积极小化n-整数倍电流在有界C2共形锥与指定的C1图形边界通过这些面积泛函的极小化问题。作为应用，我们在平均凸型假设下求解了极小曲面方程的相应Dirichlet问题。我们还将双曲空间中具有星形无穷边界的局部极小整数重流的存在唯一性推广到一大类完备共形流形中。
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 [15]. These cones are certain generalizations of hyperbolic spaces. We describe the structure of area minimizing n-integer multiplicity currents in bounded C2 conformal cones with prescribed C1 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.