论文标题
一种爆炸方法，用于规定具有固定边界的平均曲率图
A blow-up method to prescribed mean curvature graphs with fixed boundaries
论文作者
论文摘要
在本文中，我们在\ cite {sy81}中应用了一种爆炸方法，以研究$ n（n \ geq 2）$ n（n \ geq 2）$ dimensional riemannian歧管中的一大类规定的平均曲率（PMC）dirichlet问题。在此过程中，我们使用Simon \ cite {sim76}的Schauder估计方法来建立几乎最小化PMC Hypersurfaces的曲率估计。我们定义一个NC-F域，其中$ f $是从PMC方程生成的给定函数。将这种条件与足够平均凸的情况结合起来，爆破方法对这些PMC Dirichlet问题产生了相应的解决方案。例如，这种NC-F假设几乎是最佳的。还提出了我们的结果在PMC高原问题中的应用。
In this paper, we apply a blow-up method of Schoen and Yau in \cite{SY81} to study a large class of prescribed mean curvature (PMC) Dirichlet problems in $n(n\geq 2)$-dimensional Riemannian manifolds. In this process we establish curvature estimates for almost minimizing PMC hypersurfaces, using an approach of Schauder estimates from Simon \cite{Sim76}. We define an Nc-f domain, where $f$ is a given function generating from the PMC equation. Combining this condition with a sufficiently mean convex assumption the blow-up method yields corresponding solutions to these PMC Dirichlet problems. Such Nc-f assumption is almost optimal by an example. An application of our result into the PMC Plateau problem is also presented.
