The area minimizing problem in conformal cones, I
The area minimizing problem in conformal cones, I
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共形锥体中的面积最小化问题，I
DOI：
10.1016/j.jfa.2020.108827
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发表时间：
2021
影响因子：
1.7
通讯作者：
Hengyu Zhou
中科院分区：
文献类型：
--
作者：
Qiang Gao;Hengyu Zhou
本文研究了几类共形锥中的面积极小化问题。这个概念是欧氏空间中的锥和乘积流形中的柱的推广。我们定义了有界域的非闭极小（NCM）条件。在此假设和其它必要条件下，我们建立了平均凸共形锥中有界极小图的存在性。而且这些极小图也是相应面积极小化问题的解.在NCM假设下，如果非平均平移共形凸锥包含在一个更大的平均共形凸锥中，则可以求解非平均平移共形凸锥中的面积极小化问题。我们给出例子来说明，这个假设不能删除我们的主要结果。
In this paper we study the area minimizing problem in some kinds of conformal cones. This concept is a generalization of the cones in Euclidean spaces and the cylinders in product manifolds. We define a non-closed-minimal (NCM) condition for bounded domains. Under this assumption and other neces- sary conditions we establish the existence of bounded minimal graphs in mean convex conformal cones. Moreover those mini- mal graphs are the solutions to corresponding area minimizing problems. We can solve the area minimizing problem in non- mean convex translating conformal cones if these cones are contained in a larger mean convex conformal cones with the NCM assumption. We give examples to illustrate that this assumption can not be removed for our main results.