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Abstract In this paper, we aim at a reduced 2 d -model describing the observable states of the magnetization in curved thin films. Under some technical assumptions on the geometry of the thin-film, it is well-known that the demagnetizing field behaves like the projection of the magnetization on the normal to the thin film. We remove these assumptions and show that the result holds for a broader class of surfaces; in particular, for compact surfaces. We treat both the stationary case, governed by the micromagnetic energy functional, and the time-dependent case driven by the Landau–Lifshitz–Gilbert equation.
Giovanni Di Fratta (Fri,) studied this question.