We consider the Gaussian curvature conjecture of a minimal graph S over the unit disk. First of all we reduce the general conjecture to the estimating the Gaussian curvature of some Scherk’s type minimal surfaces over a quadrilateral inscribed in the unit disk containing the origin inside. As an application we improve so far the obtained upper estimates of Gaussian curvature at the point above the center. Further we obtain an optimal estimate of the Gaussian curvature at the point w over the… Expand

In this talk, I will describe some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. After a brief history and background… Expand

AbstractLet Ω be a bounded convex domain and let ω be a finite Blaschke product of order N = 1, 2, .... It is known that the elliptic differential equation
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1. Preliminaries 2. Local properties of harmonic mappings 3. Harmonic mappings onto convex regions 4. Harmonic self-mappings of the disk 5. Harmonic univalent functions 6. Extremal problems 7.… Expand