Myers-Perry时空的定域能量估计
Localized energy estimates on Myers-Perry space-times
摘要：
波动方程的局部能量估计已经越来越多地用于证明各种其他色散估计。本文主要证明了在小角动量的$(1+4)$维Myers-Perry黑洞背景下的定域能量估计。Myers-Perry时空是高维Kerr背景的推广，在高维Kerr背景中，在保持轴对称的同时，还可以有额外的旋转平面。一旦确定了所有被捕获的测地线都具有常数$r$，Tataru和第四作者开发的方法就可以适用了，该方法通过使用伪微分乘子来扰动史瓦西情况。
英文摘要：
Localized energy estimates for the wave equation have been increasingly used to prove various other dispersive estimates. This article focuses on proving such localized energy estimates on $(1+4)$-dimensional Myers-Perry black hole backgrounds with small angular momenta. The Myers-Perry space-times are generalizations of higher dimensional Kerr backgrounds where additional planes of rotation are availabile while still maintaining axial symmetry. Once it is determined that all trapped geodesics have constant $r$, the method developed by Tataru and the fourth author, which perturbs off of the Schwarzschild case by using a pseudodifferential multiplier, can be adapted.
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