On Spherical Invariance
In 1964 Pommerenke introduced the notion of linear invariant family for locally injective analytic functions defined in the unit disk of the complex plane. Following Ma and Minda (who extended this notion to spherical geometry), we consider in this paper locally injective meromorphic functions in the unit disk. More precisely, we study families of such functions for which a certain invariant, called spherical order, is finite. Several consequences on the finiteness of the spherical order are explored, in particular the connection with the Schwarzian and normal orders, and with uniform perfectness.
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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2011
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oai:scielo:S0034-742620110001000072011-08-08On Spherical InvarianceARBELÁEZ,HUGOMEJÍA,DIEGO Spherical invariance Spherical order Schwarzian derivative Normal function Uniformly perfect In 1964 Pommerenke introduced the notion of linear invariant family for locally injective analytic functions defined in the unit disk of the complex plane. Following Ma and Minda (who extended this notion to spherical geometry), we consider in this paper locally injective meromorphic functions in the unit disk. More precisely, we study families of such functions for which a certain invariant, called spherical order, is finite. Several consequences on the finiteness of the spherical order are explored, in particular the connection with the Schwarzian and normal orders, and with uniform perfectness.info:eu-repo/semantics/openAccessUniversidad Nacional de Colombia y Sociedad Colombiana de MatemáticasRevista Colombiana de Matemáticas v.45 n.1 20112011-06-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262011000100007en |
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ARBELÁEZ,HUGO MEJÍA,DIEGO |
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ARBELÁEZ,HUGO MEJÍA,DIEGO On Spherical Invariance |
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ARBELÁEZ,HUGO MEJÍA,DIEGO |
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ARBELÁEZ,HUGO |
| title |
On Spherical Invariance |
| title_short |
On Spherical Invariance |
| title_full |
On Spherical Invariance |
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On Spherical Invariance |
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On Spherical Invariance |
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on spherical invariance |
| description |
In 1964 Pommerenke introduced the notion of linear invariant family for locally injective analytic functions defined in the unit disk of the complex plane. Following Ma and Minda (who extended this notion to spherical geometry), we consider in this paper locally injective meromorphic functions in the unit disk. More precisely, we study families of such functions for which a certain invariant, called spherical order, is finite. Several consequences on the finiteness of the spherical order are explored, in particular the connection with the Schwarzian and normal orders, and with uniform perfectness. |
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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas |
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2011 |
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http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262011000100007 |
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AT arbelaezhugo onsphericalinvariance AT mejiadiego onsphericalinvariance |
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