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Asymptotics for Fermi curves of electric and magnetic periodic fields de Oliveira, Gustavo


This work is concerned with some geometrical properties of (complex) Fermi curves of electric and magnetic periodic fields. These are analytic curves in C² that arise from the study of the eigenvalue problem for periodic Schroedinger operators. More specifically, we characterize a certain class of these curves in the region of C² where at least one of the coordinates has "large" imaginary part. The new results obtained in this thesis extend previous results in the absence of magnetic field to the case of "small" magnetic field. Our theorems can be used to show that generically these Fermi curves belong to a class of Riemann surfaces of infinite genus.

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