标题： 一个关于Killing图的平均曲率方程的内部梯度估计及其应用 显示英文标题

标题： An interior gradient estimate for the mean curvature equation of Killing graphs and applications

摘要： 我们扩展了N. Korevaar和L. Simon针对平均曲率方程解的内部梯度估计，从欧几里得图的情况推广到Killing图的一般情况。 我们的主要应用是证明存在具有给定平均曲率函数的Killing图，对于连续边界数据，从而扩展了Dajczer、Hinojosa和Lira的结果。 此外，我们证明了在双曲空间中具有给定平均曲率函数和无穷远处渐近边界数据的径向图的存在性和唯一性。 显示英文摘要

摘要： We extend the interior gradient estimate due to N. Korevaar and L. Simon for solutions of the mean curvature equation from the case of Euclidean graphs to the general case of Killing graphs. Our main application is the proof of existence of Killing graphs with prescribed mean curvature function for continuous boundary data, thus extending a result due to Dajczer, Hinojosa and Lira. In addition, we prove the existence and uniqueness of radial graphs in hyperbolic space with prescribed mean curvature function and asymptotic boundary data at infinity.