Hereditary convexity for harmonic homeomorphisms Ngin-tee Koh 30C4530C6231A05convexharmonic mappingshereditary property 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 from energy-minimal diffeomorphisms of an annulus, whose existence was established in [T. Iwaniec, N.T. Koh, L.V. Kovalev, and J. Onninen, \textit{Existence of energy-minimal diffeomorphisms between doubly connected domains}, Invent. Math. \textbf{186} (2011), no. 3, 667-707], [D. Kalaj, \textit{Energy-minimal diffeomorphisms between doubly connected Riemann surfaces}, Calc. Var. Partial Differential Equations \textbf{51} (2014), no. 1--2, 465--494]. An extension of a result by Hengartner and Schober [W. Hengartner and G. Schober, \textit{Harmonic mappings with given dilatation}, J. London Math. Soc. (2) \textbf{33} (1986), no. 3, 473--483] 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. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5282 10.1512/iumj.2015.64.5282 en Indiana Univ. Math. J. 64 (2015) 231 - 243 state-of-the-art mathematics http://iumj.org/access/