Localized energy estimates for wave equations on high dimensional Schwarzschild space-times

摘要

The localized energy estimate for the wave equation is known to be a fairlyrobust measure of dispersion. Recent analogs on the $(1+3)$-dimensionalSchwarzschild space-time have played a key role in a number of subsequentresults, including a proof of Price's law. In this article, we explore similarlocalized energy estimates for wave equations on $(1+n)$-dimensionalhyperspherical Schwarzschild space-times.