Harmonic hereditary convexity (Q2040233)

The article investigates the images of the circles \(\mathbb{T}_r=\{z\in\mathbb{C}:|z|=r<1\}\) and the annulus \(\mathbb{A}_\rho=\{z\in\mathbb{C}:0<\rho<|z|<1\}\) by a harmonic diffeomorphism \(h\) and by an energy-minimal diffeomorphism \(h\) of \(\mathbb{A}_\rho\) onto a doubly connected region \(\Omega\) bounded by two convex Jordan curves in the plane. Conditions on \(h\) under which \(h(\mathbb{T}_r)\) is a strictly convex curve and \(h(\mathbb{D}_r)\) is a strictly convex domain for \(\rho<r<1\) are obtained.