Related papers: Another look at the Burns-Krantz Theorem
We prove a sharp Schwarz-type lemma for meromorphic functions with spherical derivative uniformly bounded away from zero. As a consequence we deduce an improved quantitative version of a recent normality criterion due to Grahl & Nevo and…
We discover a new Poincar\'e type phenomenon by establishing an optimal rigidity theorem for local CR mappings between circle bundles that are defined in a canonical way over (possibly reducible) bounded symmetric domains. We prove such a…
We provide a complete characterization of those non-elliptic semigroups of holomorphic self-maps of the unit disc for which the linear span of eigenvectors of the generator of the corresponding semigroup of composition operators is…
The "fundamental theorem" for algebraic $K$-theory expresses the $K$-groups of a Laurent polynomial ring $L[t,t^{-1}]$ as a direct sum of two copies of the $K$-groups of $L$ (with a degree shift in one copy), and certain "nil" groups of…
A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments).
We study local boundary behaviour of one-parameter semigroups of holomorphic functions in the unit disk. Earlier under some addition condition (the position of the Denjoy - Wolff point) it was shown in [M.D.Contreras, S.Diaz-Madrigal and…
In this note, we provide a description of the structure of homomorphisms from a finitely generated group to any torsion-free (3-dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jorgensen-Thurston…
We give new a proof of the general Brian\c{c}on-Skoda theorem about ideals of holomorphic functions by means of multivariable residue calculus. The method gives new variants of this theorem for products of ideals. Moreover, we obtain a…
We define quantum automorphism groups of a wide range of discrete structures. The central tool for their construction is a generalisation of the Tannaka-Krein reconstruction theorem. For any direct sum of matrix algebras $M$, and any…
The classical Hadamard three circle theorem is generalized to complete K\"ahler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle…
A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate…
We give a general result of finiteness for holomorphic families of Brieskorn modules constructed from a holomorphic family of one parameter degeneration of compact complex manifolds acquiring (general) singularities.
We generalize a fundamental theorem in higher dimensional value distribution theory about entire curves in subvarieties $X$ of semi-abelian varieties to the situation of the sequences of holomorphic maps from the unit disc into $X$. This…
The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings,…
In this paper, we consider the bulk plus boundary phase space for three-dimensional gravity with negative cosmological constant for a particular choice of conformal boundary conditions: the conformal class of the induced metric at the…
Let $S$ be a compact oriented surface. We construct homogeneous quasimorphisms on $Diff(S, area)$, on $Diff_0(S, area)$ and on $Ham(S)$ generalizing the constructions of Gambaudo-Ghys and Polterovich. We prove that there are infinitely many…
For Chern-Simons-matter theories in three dimensions, gauge invariance may require the Chern-Simons level k to be half-integral, in which case parity is violated. As noted by Pasquetti for abelian theories with N=2 supersymmetry, the…
The classical Julia-Wolff-Caratheodory Theorem is one of the main tools to study the boundary behavior of holomorphic self-maps of the unit disc of $\C$. In this paper we prove a Julia-Wolff-Caratheodory's type theorem in the case of the…
We develop a theory of partially defined complete positivity preservers, extending Schoenberg's classical characterization to functions defined only on discrete subsets or constrained domains. We frame the extension problem through the…
We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…