论文标题
该区域最小化的问题中的问题
The area minimizing problem in conformal cones
论文作者
论文摘要
在本文中，我们研究了在某些形式的共形锥中最小化问题的区域。这个概念是欧尔奇德空间中的锥体和产品歧管中的圆柱体的概括。我们为有限域定义了一个非关闭的最小（NCM）条件。在这个假设和其他必要条件下，我们确定了平均凸形共形锥中有界最小图的存在。而且，这些最小图是相应区域缩小问题的解决方案。如果这些锥体包含在具有NCM假设的较大的平均凸形结构锥中，我们可以解决非均值转换中的面积最小化问题。我们举例说明，对于我们的主要结果，无法删除此假设。
In this paper we study the area minimizing problem in some kinds of conformal cones. This concept is a generalization of the cones in Eulcidean spaces and the cylinders in product manifolds. We define a non-closed-minimal (NCM) condition for bounded domains. Under this assumption and other necessary conditions we establish the existence of bounded minimal graphs in mean convex conformal cones. Moreover those minimal graphs are the solutions to corresponding area minizing 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.
