相关论文: On Valiron's Theorem
We introduce three quantities related to orbits of non-elliptic continuous semigroups of holomorphic self-maps of the unit disc, the total speed, the orthogonal speed and the tangential speed and show how they are related and what can be…
In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the…
A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $n$-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis…
We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…
This paper proves the existence of a chiral map with alternating automorphism group for every hyperbolic type. We present a set of constructions using permutations for when at least one parameter is even, and call on previously known…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
The generalization of Bertrand's theorem to the case of the motion of point particle on the surface of a cone is presented. The superintegrability of such models is discussed. The additional integrals of motion are analyzed for the case of…
We prove that there is an algorithm to determine whether a tuple of elements in a toral relatively hyperbolic group G is in the automorphic orbit of the other tuple.
In this paper, we use the Carath\'eodory Convergence Theory to prove a landing theorem of rays in hyperbolic components with rational arguments. Although the proof is done in the setting of a family of entire transcendental maps with two…
We review basic theoretical concepts and developments regarding the local and itinerant properties of off-center vibronic polarons in crystals. These include the electron self-trapping and the local rotation of the species on a square…
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…
We give an overview of the theory of Cannon-Thurston maps which forms one of the links between the complex analytic and hyperbolic geometric study of Kleinian groups. We also briefly sketch connections to hyperbolic subgroups of hyperbolic…
There are many four vertex type theorems appearing in the literature, coming in both smooth and discrete flavors. The most familiar of these is the classical theorem in differential geometry, which states that the curvature function of a…
We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.
We consider holomorphic self-maps $\v$ of the unit ball $\B^N$ in $\C^N$ ($N=1,2,3,...$). In the one-dimensional case, when $\v$ has no fixed points in $\D\defeq \B^1$ and is of hyperbolic type, there is a classical renormalization…
Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…
A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is…
We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…
We consider the class of quasiprojective varieties admitting a dominant morphism onto a curve with negative Euler characteristic. The existence of such a morphism is a property of the fundamental group. We show that for a variety in this…