Abstract
The properties of electric double layers near closed-curved surfaces of arbitrary shape and genus are obtained exactly within the Debye-H\"uckel approximation by means of multiple-scattering expansions. Geometric and topological features of the electrostatics and thermodynamics emerge in a straightforward way through convergent expansions in powers of the ratio of the screening length to the principal radii of curvature. Some consequences of these results for the electrostatic contribution to the stability of structures of various shapes are considered.
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