Problems and conjectures in planar harmonic mappings

zbMath1242.30006MaRDI QIDQ648509

Daoud Bshouty, Abdallah Lyzzaik

Publication date: 22 November 2011

Published in: The Journal of Analysis (Search for Journal in Brave)

zbMATH Keywords

harmonic mappingconvex domainselliptic differential equationnon-parametric minimal surfacesanalytic dilatation

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Conformal mappings of special domains (30C20) Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20) Capacity and harmonic measure in the complex plane (30C85) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12) Connections of harmonic functions with differential equations in higher dimensions (31B35) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Second-order elliptic systems (35J47)

Related Items (13)

Univalency of convolutions of univalent harmonic right half-plane mappings ⋮ The valence of harmonic polynomials viewed through the probabilistic lens ⋮ \(\sigma _2\)-diffeomorphisms between 4-dimensional annuli ⋮ Quasihyperbolic quasi-isometry and Schwarz lemma of planar flat harmonic mappings ⋮ The inverse of a \(\sigma (z)\)-harmonic diffeomorphism ⋮ NOTE ON THE CONVOLUTION OF HARMONIC MAPPINGS ⋮ A new lower bound for the maximal valence of harmonic polynomials ⋮ Univalence criterion for harmonic mappings and Φ-like functions ⋮ Number and location of pre-images under harmonic mappings in the plane ⋮ Radius of convexity for analytic part of sense-preserving harmonic mappings ⋮ Boundary Behavior of Univalent Harmonic Mappings ⋮ Solution to an open problem on convolutions of harmonic mappings ⋮ On the zeros of random harmonic polynomials: the truncated model

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