  We consider a compact Riemannian manifold $M$ (possibly with boundary) and
$\Sigma \subset M\setminus \partial M$ an interior hypersurface (possibly with
boundary). We study observation and control from $\Sigma$ for both the wave and
heat equations. For the wave equation, we prove controllability from $\Sigma$
in time $T$ under the assumption $(\mathcal{T}GCC)$ that all generalized
bicharacteristics intersect $\Sigma$ transversally in the time interval
$(0,T)$. For the heat equation we prove unconditional controllability from
$\Sigma$. As a result, we obtain uniform lower bounds for the Cauchy data of
Laplace eigenfunctions on $\Sigma$ under $\mathcal{T}GCC$ and unconditional
exponential lower bounds on such Cauchy data.
