Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Generalized John disks

100%

Guo C.-Y., Koskela P.

Open Mathematics

2014

tom 12

nr 2

349-361

We establish the basic properties of the class of generalized simply connected John domains.

Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues

52%

Krushkal S.

Open Mathematics

2007

tom 5

nr 3

551-580

The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to $$\widehat{\mathbb{C}}$$ are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = {z: |z| > 1} can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely, in the norm on the space of Schwarzian derivatives. Applications of this result to Fredholm eigenvalues are given. We also solve the old Kühnau problem on an exact lower bound in the inverse inequality estimating k(f) by ϰ(f), and in the related Ahlfors inequality.

Ograniczanie wyników

2 Open Mathematics

1 Guo C.-Y.

1 Koskela P.

1 Krushkal S.

1 2014

1 2007

Wyniki wyszukiwania

Generalized John disks

Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues