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In this paper, we present an alternative and elementary proof of a sharp version of the classical boundary Schwarz lemma by Frolova et al. with initial proof via analytic semigroup approach and Julia-Caratheodory theorem for univalent holomorphic self-mappings of the open unit disk $mathbb Dsubset mathbb C$. Our approach has its extra advantage to get the extremal functions of the inequality in the boundary Schwarz lemma.
In this paper, we generalize a recent work of Liu et al. from the open unit ball $mathbb B^n$ to more general bounded strongly pseudoconvex domains with $C^2$ boundary. It turns out that part of the main result in this paper is in some certain sense
In this paper we establish several invariant bounda
We prove a Schwarz lemma for a domain E in 3-dimensional complex space that arises in connection with a problem in H infinity control theory. We describe a class of automorphisms of E and determine the distinguished boundary of E. We obtain a type of
We study the smoothness of the Siciak-Zaharjuta extremal function associated to a convex body in $mathbb{R}^2$. We also prove a formula relating the complex equilibrium measure of a convex body in $mathbb{R}^n$ to that of its Robin indicatrix. The main tool we use are extremal ellipses.
In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish related Schwarz type lemmas fo