Hyperbolically convex constricted domains |
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Authors: | Juan Arango |
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Affiliation: | Escuela de Matemáticas, Universidad Nacional de Colombia, Calle 59 A No. 63-020, Bloque 43, Medellín, Colombia |
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Abstract: | A subdomain G in the unit disk D is called hyperbolically convex if the non-euclidean segment between any two points in G also lies in G. We introduce the concept of constricted domain relative to the hyperbolic geometry of D and prove that a hyperbolic convex domain is constricted if and only if it is not a quasidisk. Also examples are given to illustrate these ideas. |
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Keywords: | Hyperbolically convex Constricted domain Quasidisk Hyperbolic geometry |
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