Level Lines of Harmonic Functions Related to Some Abelian Integrals. / V. V. Fufaev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 1. P. 16-25 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 15-23].
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.
Key words: elliptic integral, quadratic differential.