Maximal $L^p$-regularity of Laplace-Beltrami operator $\Delta$ on closed manifold

Question

It's well-known that the Dirichlet Laplacian $\Delta$ on flat domain is R-sectorial on $\Sigma_{\pi}$ in $L^p$ space for all $p\in (1,\infty)$.

I'm wondering if the Laplace-Beltrami operator $\Delta$ on closed manifold has the same property?