| Abstract: |
| Consider the metric cone $X=C(Y)=(0,\infty)_r\times Y$ with the metric $g=dr^2+r^2h$ where the cross section $Y$ is
a compact $(n-1)$-dimensional Riemannian manifold $(Y,h)$. Let $\Delta_g$ be the Friedrich extension positive Laplacian on $X$ and let $\Delta_h$ be the positive Laplacian on $Y$, and consider the operator $\mathcal{L}_V=\Delta_g+V_0 r^{-2}$ where
$V_0\in C^\infty(Y)$ such that $\Delta_h+V_0+(n-2)^2/4$ is a strictly positive operator on $L^2(Y)$. We prove the global-in-time Strichartz estimates without loss for the Schrodinger and wave equation associated with the operator $\mathcal{L}_V.$ This work is jointed with Junyong Zhang. |
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