Title: Interior transmission eigenvalue problems on compact manifolds with boundary conductivity parameters,
Abstract: In this paper, we consider an interior transmission eigenvalue (ITE) problem
on some compact $C^{\infty }$-Riemannian manifolds with a common smooth
boundary. In particular, these manifolds may have different topologies, but we
impose some conditions of Riemannian metrics, indices of refraction and
boundary conductivity parameters on the boundary. Then we prove the
discreteness of the set of ITEs, the existence of infinitely many ITEs, and its
Weyl type lower bound. For our settings, we can adopt the argument by
Lakshtanov and Vainberg, considering the Dirichlet-to-Neumann map. As an
application, we derive the existence of non-scattering energies for
time-harmonic acoustic equations. For the sake of simplicity, we consider the
scattering theory on the Euclidean space. However, the argument is applicable
for certain kinds of non-compact manifolds with ends on which we can define the
scattering matrix.