Quasikonforme Fortsetzbarkeit, Fredholmsche Eigenwerte und Grunskysche Koeffizientenbedingungen

The asymptotic Teichmüller space and the asymptotic Grunsky map

“…On the other hand, since t 0 µ/ µ ∞ is extremal with a degenerating Hamilton sequence in A 2 , we conclude that G[t 0 µ/ µ ∞ ] T = |t 0 |. Now, by a previous result [18,26,28], we have G[μ] T = G[t 0 µ/ µ ∞ ] T = |t 0 |. Thus, we conclude by theorem 7.1 and (7.8) (see also [15]) thatμ has a Hamilton sequence in A 2 .…”

On a modification of the Poisson integral operator

“…By [24,Theorem 4.4.2], the set Λ * (Γ) of all eigenvalues of a quasicircle Γ ⊂ C coincides with the set Λ * γ , where γ is a welding homeomorphism of Γ. Therefore, Theorem 3.1 is closely related to various results involving these constants obtained by Kühnau ([15], [16], [17]), Schiffer ([29]) and Krushkal ([6], [7], [8,Sect. 2]); see also the survey article by Krushkal [9, p. 528] and the references given there.…”

On Grunsky inequalities and the exact domain of variability of the Grunsky functional

“…Following Kühnau [Ku3] and Pommerenke [Po1], we denote by Σ k the class of univalent functions f in Σ 0 with G(f ) ≤ k. Clearly, Σ(k) ⊂ Σ k , and Σ k = Σ(k) unless k = 0. The following result solves the extremal problem in the subclass Σ k for x ∈ l 2 0 .…”