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The aim of this paper is to establish uniform estimates of the spectrum'sbottom of the Neumann realization of $(i\nabla+q\A)^2$ on a bounded open set$\Om$ with smooth boundary when $|\nabla\times\A|=1$ and $q\to+\infty$. Thisproblem was motivated by a question occuring in the theory of liquid crystalsand appears also in superconductivity questions in large domains.

Uniform spectral estimates for families of Schrodinger operators with magnetic field of constant intensity and applications