Our main result is a description of the boundary of the parameter space of classical Schottky groups affording two parabolic generators within the larger parameter space of all Schottky groups with two parabolic generators. This boundary is surprisingly different from that of the larger space. It is analytic while the boundary of the larger space is fractal. Approaching the boundary of the smal...

A Carleman estimate for a differential operator P is a weighted energy estimate with a weight of exponential form exp(τφ) that involves a large parameter, τ > 0. The function φ and the operator P need to fulfill some sub-ellipticity properties that can be achieved for instance by choosing φ = exp(αψ), involving a second large parameter, α > 0, with ψ satisfying some geometrical conditions. The ...