论文标题
关于度量陷阱和边界的相互作用
On the interaction of metric trapping and a boundary
论文作者
论文摘要
通过考虑两个末端的扭曲产物歧管，我们证明了当公制陷阱与边界相互作用时可能发生的分叉。在这个高度对称的示例中，随着边界通过被困的集合，一个从非捕获的场景中进行的，其中无损局部能量估计值可用于波方程到稳定的捕获射线的情况，在这些情况下，除了丢失的对数衰减量以外，所有其他均已丢失。
By considering a two ended warped product manifold, we demonstrate a bifurcation that can occur when metric trapping interacts with a boundary. In this highly symmetric example, as the boundary passes through the trapped set, one goes from a nontrapping scenario where lossless local energy estimates are available for the wave equation to the case of stably trapped rays where all but a logarithmic amount of decay is lost.
