  The boundary double layer potential, or the Neumann-Poincare operator, is
studied on the Sobolev space of order 1/2 along the boundary, coinciding with
the space of charges giving rise to double layer potentials with finite energy
in the whole space. Poincare's program of studying the spectrum of the boundary
double layer potential is developed in complete generality, on closed Lipschitz
hypersurfaces in Euclidean space. Furthermore, the Neumann-Poincare operator is
realized as a singular integral transform bearing similarities to the
Beurling-Ahlfors transform in 2D. As an application, bounds for the spectrum of
the Neumann-Poincare operator are derived from recent results in
quasi-conformal mapping theory, in the case of planar curves with corners.
