5 citations · 12 across the 9 of their papers we have counts for
8 papers · 1 filter
Blow--up Solutions of Liouville's Equation and Quasi--Normality
Jürgen Grahl, Daniela Kraus, Oliver Roth
We prove that the family of all meromorphic functions on a domain with the property that the spherical area of the image domain $f(D)…
Differential inequalities and a Marty-type criterion for quasi-normality
Jürgen Grahl, Tomer Manket, Shahar Nevo
We show that the family of all holomorphic functions in a domain satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\le C \qquad \mbox{ for all } z\in D$$ (where is a natural numbe…
Quasi-normality induced by differential inequalities
Jürgen Grahl, Shahar Nevo
We show that the family of all meromorphic functions in a domain satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\ge C \qquad \mbox{ for all } z\in D$$ (where is a…
Differential inequalities and quasi-normal families
Roi Bar, Jürgen Grahl, Shahar Nevo
We show that a family of meromorphic functions in a domain satisfying $$\frac{|f^{(k)}|}{1+|f^{(j)}|^α}(z)\ge C \qquad \mbox{for all} z\in D \mbox{and all} f\in {\ca…
An extension of one direction in Marty's normality criterion
J. Grahl, S. Nevo
We prove an extension of one direction in Marty's theorem where the spherical derivative is replaced by a more general quantity involving higher derivatives.
A Non explicit counterexample to a problem of quasi-normality
Shahar Nevo, Xuecheng Pang
In 1986, S.Y. Li and H.Xie proved the following theorem:Let k>=2 and let F be a family of functions meromorphic in some domain D, all of whose zeros are of multiplicity at least k.…