相关论文: The Schwarz-Pick lemma of high order in several va…
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings between the unit balls in complex spaces. This extends the classical Schwarz-Pick lemma and the related result proved by Pavlovic.
In this paper we prove a Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of R^n.
The celebrated Schwarz-Pick lemma for the complex unit disk is the basis for the study of hyperbolic geometry in one and in several complex variables. In the present paper, we turn our attention to the quaternionic unit ball B. We prove a…
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
This paper establishes a sharp Schwarz-Pick type inequality for real-valued invariant harmonic functions defined on the complex unit ball $\mathbb B^n$. The proof of this main result simultaneously provides a solution to a natural extension…
Based on the recently proved Khavinson conjecture, we establish an inequality of Schwarz-Pick type for harmonic functions on the unit ball of $\mathbb{R}^n$.
In this paper, we will give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk. Our main results are generalizations of results of Colonna for planar harmonic…
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order,…
The aim of this article is to give an elementary proof of the fact that the Schwarz-Pick Lemma follows from the Ahlfors-Schwarz-Pick Lemma.
In this note we establish a Schwarz type inequality for holomorphic mappings between unit balls $B_n$ and $B_m$ in corresponding complex spaces.
In this paper, we prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary…
The well-known Schwarz-Pick lemma states that any analytic mapping $\phi$ of the unit disk $U$ into itself satisfies the inequality $$|\phi'(z)|\leq \frac{1-|\phi(z)|^2}{1-|z|^2}, \quad z\in U.$$ This estimate remains the same if we…
We obtain Schwarz-Pick lemma for $(\alpha, \beta)$-harmonic functions u in the disc, where $\alpha$ and $\beta$ are complex parameters satisfying $\Re \alpha + \Re \beta > -1$. We prove sharp estimate of derivative at the origin for such…
The Schwarz--Pick lemma is a fundamental result in complex analysis. It is well-known that Yau generalized it to the higher dimensional manifolds by applying his maximum principle for complete Riemannian manifolds. Jeffres obtained Schwarz…
The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions…
In this paper, we first establish the Schwarz-Pick lemma of higher-order and apply it to obtain a univalency criteria for planar harmonic mappings. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic…
In this paper we prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, our result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a…
We establish some inequalities of Schwarz-Pick type for harmonic and hyperbolic harmonic functions on the unit ball of and we disprove a recent conjecture of Liu [Schwarz-Pick Lemma for Harmonic Functions, International Mathematics Research…
We obtain upper bounds for the norm of the Schwarzian derivative of convex holomorphic mappings defined on the polydisk and the unit ball in $\mathbb{C}^n$. For coordinate-wise convex mappings on the polydisk, we derive a sharp estimate…
We prove a Schwarz type lemma for harmonic mappings between the unit and a geodesic line in a Riemenn surface.