Related papers: Two boundary rigidity results for holomorphic maps
In this paper we establish several invariant boundary versions of the (infinitesimal) Schwarz-Pick lemma for conformal pseudometrics on the unit disk and for holomorphic selfmaps of strongly convex domains in $\mathbb C^N$ in the spirit of…
In this article, we characterize the holomorphic mappings from $B_{\ell_p^n}\times\mathbb{D}^{m}$ into $\mathbb{D}^{m}$ for $p\in \{2,\infty\}$. In addition, we give a simple proof for the boundary Schwarz lemma for vector valued…
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…
We present a form of Schwarz's lemma for holomorphic maps between convex domains $D_1$ and $D_2$. This result provides a lower bound on the distance between the images of relatively compact subsets of $D_1$ and the boundary of $D_2$. This…
We first prove a Boundary Schwarz lemma for holomorphic disks on the unit ball in $\mathbb{C}^n$. Further by using a Schwarz lemma for minimal conformal disks of Forstneri\v c and Kalaj (F.~Forstneri{\v{c}} and D.~Kalaj. \newblock…
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 symmetrized bidisc ${\textbf{G}}_{2}$ is defined by $${\textbf{G}}_{2}:=\{(z_1+z_2,z_1z_2)\in\mathbb{C}^2: |z_1|<1,|z_2|<1,\; z_1,z_2\in\mathbb{C}\}.$$ It is a bounded inhomogeneous pseudoconvex domain without $\mathcal{C}^1$ boundary,…
Suppose that $M$ is a K\"ahler manifold with a pole such that its holomorphic sectional curvature is bounded from below by a constant and its radial sectional curvature is also bounded from below. Suppose that $N$ is a strongly pseudoconvex…
The Schwarz lemmas are well-known characterizations for holomorphic maps and we exhibit two examples of their applications. For a sequence family of biholomorphisms $f_j$, it is useful to determine the location of $f_j(q)$ for a fixed point…
The main purpose of this paper is to develop some methods to investigate the Schwarz type lemmas of holomorphic mappings and pluriharmonic mappings in Hilbert and Banach spaces. Initially, we extend the classical Schwarz lemmas of…
In this paper, we establish a boundary Schwarz lemma for solutions to non-homogeneous biharmonic equations.
We establish some Schwarz type Lemmas for mappings defined on the unit disk with bounded Laplacian. Then we apply these results to obtain boundary versions of the Schwarz lemma.
We prove a Schwarz-type lemma for noncompact manifolds with possibly noncompact boundary. The result is a consequence of a suitable form of the weak maximum principle of independent interest. The paper is enriched with applications to…
In this paper, we derive some $\partial\overline{\partial}$-Bochner formulas for holomorphic maps between Hermitian manifolds. As applications, we prove some Schwarz lemma type estimates, rigidity and degeneracy theorems. For instance, we…
The most classical version of the Schwarz lemma involves the behavior at the origin of a bounded, holomorphic function on the disc. Pick's version of the Schwarz lemma allows one to move the origin to other points of the disc. In the…
Motivated by recent papers \cite{For-Rong 2021} and \cite{Ng-Rong 2024} we prove a boundary Schwarz lemma (Burns-Krantz rigidity type theorem) for non-smooth boundary points of the polydisc and symmetrized bidisc. Basic tool in the proofs…
It is well-known that the classical Schwarz lemma yields an explicit comparison of two Hermitian metrics with uniform constant negative curvature bounds through holomorphic maps between complex manifolds. In this paper, we establish Schwarz…
We prove a boundary version of the strong form of the Ahlfors-Schwarz lemma with optimal error term. This result provides nonlinear extensions of the boundary Schwarz lemma of Burns and Krantz to the class of negatively curved conformal…
We survey a number of recent generalizations and sharpenings of Nehari's extension of Schwarz' lemma for holomorphic self-maps of the unit disk. In particular, we discuss the case of infinitely many critical points and its relation to the…
In this paper, we give a general boundary Schwarz lemma for holomorphic mappings between unit balls in any dimensions. It is proved that if the mapping $f\in C^{1+\alpha}$ at $z_0\in \partial \mathbb B^n$ with $f(z_0)=w_0\in \partial…