Abstract
We study hereditary properties of convexity for planar harmonic homeomorphisms on a disk and an annulus. A noteworthy class of examples with the hereditary property arises fromenergy-minimal diffeomorphismsof an annulus, whoseex- istence was established in (9,11). An extension of a result by Hengartner and Schober (8) to an annulus is used to deduce the boundary behavior of a harmonic mapping from an annulus into a doubly-connected region bounded by two convex Jordan curves.
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