Geodesic
Harmonic Mappings onto Convex Domains
Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1489-1530

Voir la notice de l'article provenant de la source Cambridge University Press

Let D be a simply-connected domain and w 0 a fixed point of D. Denote by SD the set of all complex-valued, harmonic, orientation-preserving, univalent functions f from the open unit disk U onto D with f(0) = w 0. Unlike conformai mappings, harmonic mappings are not essentially determined by their image domains. So, it is natural to study the set SD .In Section 2, we give some mapping theorems. We prove the existence, when D is convex and unbounded, of a univalent, harmonic solution f of the differential equation where a is analytic and |a| < 1, such that f(U) ⊂ D and 
Abu-Muhanna, Yusuf; Schober, Glenn. Harmonic Mappings onto Convex Domains. Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1489-1530. doi: 10.4153/CJM-1987-071-4
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