论文标题
圆环的规定平均曲率方程式
Prescribed mean curvature equation on torus
论文作者
论文摘要
在一个维度上考虑了圆环上规定的平均曲率问题。在本文中，我们证明了在$ n $维圆环$ \ mathbb {t}^n $上存在图的平均曲率向量，其平均曲率向量等于给定矢量场的正常成分，满足了Sobolev Norm，Integrated Value和单调性的适当条件。
Prescribed mean curvature problems on the torus has been considered in one dimension. In this paper, we prove the existence of a graph on the $n$-dimensional torus $\mathbb {T}^n$, the mean curvature vector of which equals the normal component of a given vector field satisfying suitable conditions for a Sobolev norm, the integrated value, and monotonicity.
