Related papers: Schwarz Lemma for the tetrablock

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…

We realise Buchweitz and Flenner's semiregularity map (and hence a fortiori Bloch's semiregularity map) as the tangent of a morphism of derived moduli functors. An immediate consequence is that it annihilates all obstructions (not just…

We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct $d$-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant constructed…

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…

Using effective field theory methods, we derive the Carrollian analog of the geodesic action. We find that it contains both `electric' and `magnetic' contributions that are in general coupled to each other. The equations of motion…

Let $f$ be a holomorphic, or even meromorphic, function on the unit disc. Plessner's theorem then says that, for almost every boundary point $\zeta $, either (i) $f$ has a finite nontangential limit at $\zeta $, or (ii) the image $f(S)$ of…

This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using…

One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous…

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…

For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…

In this paper, we present formulas for the edge zeta function and the second weighted zeta function with respect to the group matrix of a finite abelian group $\Gamma $. Furthermore, we give another proof of Dedekind Theorem for the group…

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.

In the paper we discuss the problem of existence, uniqueness and extension through the boundary of left inverses to complex geodesics in Lempert domains. We concentrate on special left inverses (so called Lempert left inverses)…

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis,…

The Lempert function for several poles $a_0, ..., a_N$ in a domain $\Omega$ of $\mathbb C^n$ is defined at the point $z \in \Omega$ as the infimum of $\sum^N_{j=0} \log|\zeta_j|$ over all the choices of points $\zeta_j$ in the unit disk so…

In order to classify and understand the spacetime structure, investigation of the geodesic motion of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of…

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 prove a ``general shrinking lemma'' that resembles the Schwarz--Pick--Ahlfors Lemma and its many generalizations, but differs in applying to maps of a finite disk into a disk, rather than requiring the domain of the map to be complete.…

We show here that the fundamental lemma for twisted endoscopy, now proved for the unit elements in the spherical Hecke algebras, implies the fundamental lemma for all elements of these Hecke algebras. The proof, whose idea is due to Arthur,…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…