  The problem of obtaining the lower bounds on the restriction of Laplacian
eigenfunctions to hypersurfaces inside a compact Riemannian manifold $(M,g)$ is
challenging and has been attempted by many authors \cite{BR, GRS, Jun, ET}.
This paper aims to show that if $(M,g)$ is assumed to be a negatively curved
surface then one can get the corresponding restricted lower bounds, as well as
quantitative improvement of restricted bounds for Neumann data.
