Abstract: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.

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中文翻译：

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关于度量陷阱和边界的相互作用

摘要：通过考虑两端扭曲的产品流形，我们展示了当度量陷阱与边界相互作用时可能发生的分叉。在这个高度对称的例子中，当边界通过陷获集时，人们从非陷陷场景（其中无损局部能量估计可用于波动方程）到稳定陷获射线的情况，其中除对数衰减之外的所有衰减都丢失了。

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