Normal families of holomorphic mappings into complex projective space concerning shared hyperplanes

2 Quantum Normal Families : Normal Families of Holomorphic Functions and Mappings on a Banach Space

The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinitedimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical derivatives, and other geometric properties are derived. Montel-type theorems are established. A number of different topologies on spaces of holomorphic mappings are c...

On Abelian Families and Holomorphic Normal Projective Connections

1.) Pm(C), 2.) smooth abelian families, 3.) manifolds with universal covering Bm(C). Here Bm(C) denotes the ball in C , the non compact dual of Pm(C) in the sense of hermitian symmetric spaces. The second point inlcudes the flat case of an abelian manifold. Any compact Riemann surface admits a holomorphic normal projective connection, this is the famous uniformization theorem. Kobayashi and Och...

Normal holomorphic maps from C to a projective space

A theorem of A. Ostrowski describing meromorphic functions f such that the family {f(λz) : λ ∈ C∗} is normal, is generalized to holomorphic maps from C∗ to a projective space. MSC 2010: 30D45, 32A19.

Normal Criteria for Families of Meromorphic Function concerning Shared Values

Let k be a positive integer and let F be a family of meromorphic functions in the plane domain D all of whose zeros with multiplicity at least k. Let P = apz p + · · ·+a2z +z be a polynomial, ap, a2 6= 0 and p = deg(P ) ≥ k+2. If, for each f, g ∈ F , P (f)G(f) and P (g)G(g) share a non-zero constant b in D, where G(f) = f (k) + H(f) be a differential polynomial of f satisfying w deg |H ≤ k l+1 ...

Normal Criteria of Function Families Concerning Shared Values