Partial Data Calder\'on Problems for $L^{n\mathrm{/}2}$ Potentials on Admissible Manifolds

We solve the partial data Calder'on problem on conformally transversallly anisotropic (CTA) manifolds with $L^{n\mathrm{/}2}$ potentials - on par with sharp unique continuation result of \cite{JerKen}. A trivial consequence of this is the sharp regularity improvement to the result of Kenig-Sj"ostrand-Uhlmann \cite{ksu}. This is done by constructing a “Green’s function” which possesses both desirable boundary conditions {\em and} satisfies semiclassical type estimates in the suitable $L^p$ spaces. No Carleman estimates were used in the writing of this article which makes it starkly different from the traditional approaches based on \cite{BukUhl} and \cite{ksu}.