论文标题
用固体锥的歧管上的一个单数山菜问题
A singular Yamabe problem on manifolds with solid cones
论文作者
论文摘要
我们研究了具有非紧密边界的非紧凑型riemannian歧管上的共形度量的存在，它们作为度量空间完整，并且内部具有负恒定标量曲率，而边界上的负恒定平均曲率为负。这些指标是通过从某些在广义固体锥体上局部建模的N维空间中去除D维的亚策略来获得的平滑歧管上构建的。当且仅当D>（n-2）/2时，我们就证明了这种指标的存在。我们的主要定理的灵感来自Aviles-McOwen和Loewner-Nirenberg在文献中被称为“单一Yamabe问题”的经典结果。
We study the existence of conformal metrics on non-compact Riemannian manifolds with non-compact boundary, which are complete as metric spaces and have negative constant scalar curvature in the interior and negative constant mean curvature on the boundary. These metrics are constructed on smooth manifolds obtained by removing d-dimensional submanifolds from certain n-dimensional compact spaces locally modelled on generalized solid cones. We prove the existence of such metrics if and only if d>(n-2)/2. Our main theorem is inspired by the classical results by Aviles-McOwen and Loewner-Nirenberg known in the literature as the "singular Yamabe problem".
