8 papers · 1 filter
Hyperbolic-type metrics in space
Aimo Hinkkanen, Poranee Khayo
We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenk…
Value sharing and Stirling numbers
Aimo Hinkkanen, Ilpo Laine
Let be an entire function and a linear differential polynomial in with constant coefficients. Suppose that , , and share a meromorphic function …
Maximum and average valence of meromorphic functions
Aimo Hinkkanen, Joseph Miles
If is a meromorphic function from the complex plane to the extended complex plane , for let be the maximum number of solu…
A geometric property of quadrilaterals
Efstathios Konstantinos Chrontsios Garitsis, Aimo Hinkkanen
Quadrilaterals in the complex plane play a significant part in the theory of planar quasiconformal mappings. Motivated by the geometric definition of quasiconformality, we prove th…
On the hyperbolic metric of certain domains
Aimo Hinkkanen, Matti Vuorinen
We prove that if is a compact subset of the unit disk in the complex plane, if contains a sequence of distinct points for such that $\l…
Asymptotic functions of entire functions
Aimo Hinkkanen, Joseph Miles, John Rossi
If is an entire function and is a complex number, is said to be an asymptotic value of if there exists a path from to infinity such that tends to…
Quasiregular families bounded in and elliptic estimates
Aimo Hinkkanen, Gaven Martin
We prove that a family of quasiregular mappings of a domain which are uniformly bounded in for some form a normal family. From this we show how an elliptic estimate…
Equilateral triangle skew condition for quasiconformality
Colleen Ackermann, Peter Haïssinsky, Aimo Hinkkanen
We characterize quasiconformal mappings in terms of the distortion of the vertices of equilateral triangles.