  In geophysical environments, wave motions that are shaped by the action of
gravity and global rotation bear the name of gravito-inertial waves. We present
a geometrical description of gravito-inertial surface waves, which are
low-frequency waves existing in the presence of a solid boundary. We consider
an idealized fluid model for an incompressible fluid enclosed in a smooth
compact three-dimensional domain, subject to a constant rotation vector. The
fluid is also stratified in density under a constant Brunt-V{\"a}is{\"a}l{\"a}
frequency. The spectral problem is formulated in terms of the pressure, which
satisfies a Poincar\'e equation within the domain, and a Kelvin equation on the
boundary. The Poincar\'e equation is elliptic when the wave frequency is small
enough, such that we can use the Dirichlet-to-Neumann operator to reduce the
Kelvin equation to a pseudo-differential equation on the boundary. We find that
the wave energy is concentrated on the boundary for large covectors, and can
exhibit surface wave attractors for generic domains. In an ellipsoid, we show
that these waves are square-integrable and reduce to spherical harmonics on the
boundary.
