论文标题
规定的标量和边界平均曲率问题以及渐近欧几里德歧管上具有内部边界的Yamabe分类
A prescribed scalar and boundary mean curvature problem and the Yamabe classification on asymptotically Euclidean manifolds with inner boundary
论文作者
论文摘要
我们考虑在给定的非阳性标量曲率和非阳性边界平均值曲率上在给定的非阳性标量曲率和非阳性的边界曲率上找到度量的问题。我们根据存在解决方案的解决方案的零集合集合零集的形式，并利用此结果来确定这些歧管中指标的Yamabe分类，以确定零的Yamabe分类。
We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean curvature on an asymptotically Euclidean manifold with inner boundary. We obtain a necessary and sufficient condition in terms of a conformal invariant of the zero sets of the target curvatures for the existence of solutions to the problem and use this result to establish the Yamabe classification of metrics in those manifolds with respect to the solvability of the prescribed curvature problem.
