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Article

Level lines of harmonic functions related to some Abelian integrals

Moscow University Mathematics Bulletin. 2017. Vol. 72. No. 1. P. 15-23.
Fufaev V.

The geometry of level lines of harmonic functions being real parts of some Abelian integrals is studied. Such harmonic functions appear in the study of asymptotics of solutions to second-order differential equations, and the corresponding level lines are related both to the distribution of eigenvalues of a non-self-adjoint Sturm–Liouville problem and to location of trajectories of the corresponding quadratic differentials.