Abstract
For a harmonic map transforming the contour of an angle of the boundary into a rectilinear segment of the boundary , the behavior near the vertex of the specified angle is investigated. The behavior of the inverse map near the preimage of the vertex is investigated as well. In particular, we prove that if ϕ is the value of the angle at which a ray is issued from the vertex, and θ is the value of the angle at which its image leaves the vertex's, then the dependence of θ on ϕ is described by a discontinuous function. Thus, such a behavior of the harmonic map qualitatively differs from the behavior of the corresponding conformal map: for the latter one, the dependence is described by a linear function.
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