Displaying similar documents to “Complex calculus of variations”

Hyperbolically 1-convex functions

William Ma, David Minda, Diego Mejia (2004)

Annales Polonici Mathematici

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There are two reasonable analogs of Euclidean convexity in hyperbolic geometry on the unit disk 𝔻. One is hyperbolic convexity and the other is hyperbolic 1-convexity. Associated with each type of convexity is the family of univalent holomorphic maps of 𝔻 onto subregions of the unit disk that are hyperbolically convex or hyperbolically 1-convex. The class of hyperbolically convex functions has been the subject of a number of investigations, while the family of hyperbolically 1-convex...