Strichartz estimates for the Klein-Gordon equation in a conical singular space

Abstract

Consider a conical singular space $X=C(Y)=(0,\infty {)}_r\times Y$ with the metric $g=\mathrm{d}{r}^2+r^{2}h$, where the cross section $Y$ is a compact $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the Klein-Gordon equations with inverse-square potentials in the space $X$, proving in particular global-in-time Strichartz estimates in this setting.

44 pages. Comments are welcome

References in corpus (1)

• The Riesz transform for homogeneous Schrödinger operators on metric cones