Localized energy estimates for wave equations on (1 + 4)-dimensional myers-perry space-times

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 available 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.