相关论文: Carath\'eodory's Theorem and moduli of local conne…

Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.

The classical Julia-Wolff-Carath{\'e}odory Theorem characterizes the behaviour of the derivative of an analytic self-map of a unit disc or of a half-plane of the complex plane at certain boundary points. We prove a version of this result…

We prove relations among the classes of certain divisors on the moduli spaces of curves with marked points, generalizing the Brill-Noether Ray Theorem of Eisenbud and Harris.

In the 1970s, the collar theorem was proven, establishing the existence of uniform tubular neighborhoods of simple closed geodesics on compact surfaces, whose widths depend only on the lengths of the geodesics and the lower bound of the…

We prove that for any closed surface of genus at least four, and any punctured surface of genus at least two, the space of ending laminations is connected. A theorem of E. Klarreich implies that this space is homeomorphic to the Gromov…

We construct an arithmetic analogue of the quantum local systems on the moduli of curves, and study its basic structure. Such an arithmetic local system gives rise to a uniform way of assigning a Galois cohomology class of the first…

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem.

We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded…

In this paper, we prove that if a Carath\'eodory hyperbolic analytic space $X$ is $C_X$-complete, then its natural topology is induced by the Carath\'eodory distance on $X$. This is an improvement of Sibony's result, which concludes the…

We prove that the first homology group of every planar locally transitive finite graph $G$ is a finitely generated ${\rm Aut}(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs.…

A theorem of Picard's type is proved for entire holomorphic mappings into complex projective varieties. This theorem has local character in the sense that the existence of Julia directions can be proved under a natural additional…

Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.

The path spaces of a directed graph play an important role in the study of graph $\css$. These are topological spaces that were originally constructed using groupoid and inverse semigroup techniques. In this paper, we develop a simple,…

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…

A proof of Petri's general conjecture on the unobstructedness of linear systems on a general curve is proposed, using only the local properties of the deformation space of the pair (curve, line bundle).

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as…

We intoduce a local version of the Jordan-Brouwer separation theorem and deduce some global statements, some of which may follow from known results, but the technique is new.

We study hyperelliptic curves y^2=f(x) over local fields of odd residue characteristic. We introduce the notion of a "cluster picture" associated to the curve, that describes the p-adic distances between the roots of f(x), and show that…

A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved.

We give a simple generalisation of a theorem of Morita, which leads to a great number of relations among tautological classes on moduli spaces of curves.