Title: Global-in-time Strichartz estimates and cubic Schrodinger equation on metric cone,
Abstract: We study the Strichartz estimates for Schrödinger equation on a metric cone
$X$, where the metric cone $X=C(Y)=(0,\infty)_r\times Y$ and the cross section
$Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. The equipped
metric on $X$ is given by $g=dr^2+r^2h$, and let $\Delta_g$ be the Friedrich
extension positive Laplacian on $X$ and $V=V_0 r^{-2}$ where
$V_0\in\CC^\infty(Y)$ is a real function such that the operator
$\Delta_h+V_0+(n-2)^2/4$ is a strictly positive operator on $L^2(Y)$. We
establish the full range of the global-in-time Strichartz estimate without loss
for the Schödinger equation associated with the operator $\LL_V=\Delta_g+V_0
r^{-2}$ including the endpoint estimate both in homogeneous and inhomogeneous
cases. As an application, we study the well-posed theory and scattering theory
for the Schödinger equation with cubic nonlinearity on this setting.