A remark on certain -valent functions.
We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
We give a Schwarz lemma on complex ellipsoids.
We derive a sharp bound for the modulus of the Schwarzian derivative of concave univalent functions with opening angle at infinity less than or equal to πα, α ∈ [1,2].