Products of Hyperbolic Metric Spaces

Let (X _i d _i ), i=1,2, be proper geodesic hyperbolic metric spaces. We give a general construction for a 'hyperbolic product' X ₁× _h X ₂ which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.     

Asymptotic Values of Hyperbolic Monopoles

It is shown that many hyperbolic monopoles can be distinguishedfrom each other via their asymptotic values in contrast to thecase of Euclidean monopoles.     

Constructive Axiomatization of Plane Hyperbolic Geometry

We provide a universal axiom system for plane hyperbolic geometry in a firstorder language with two sorts of individual variables, ‘points’ (upper‐case) and ‘lines’ (lowercase), containing three individual constants, A₀, A₁, A₂, standing for three non‐collinear points, two binary operation symbols, φ and ι, with φ(A, B) = l to be interpreted as ‘𝓁 is the line joining A and B’ (provided that A ≠ B, an arbitrary line, otherwise), and ι(g, h) = P to be interpreted as 𝓁P is the point of intersection of g and h (provided that g and h are distinct and have a point of intersection, an arbitrary point, otherwise), and two binary operation symbols, π₁(P, 𝓁) and —₂(P, 𝓁), with π_i(P, 𝓁) = g (for i = 1, 2) to be interpreted as ‘g is one of the two limiting paralle lines from P to 𝓁 (provided that P is not on 𝓁, an arbitrary line, otherwise).     

Electrostatics, Hyperbolic Geometry and Wandering Vectors

A family of planar discrete electrostatic systems on the unitcircle with finitely atomic external fields is considered. Thegeometry of particles in the external field yielding a givenminimum energy configuration is studied. As an application,the wandering vectors of the shift operator in the Dirichletspaces associated with finitely atomic measures are also studied.In particular, the zero locus of a wandering vector is discussed.     

Isometry Groups of Proper Hyperbolic Spaces

Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not elementary then for every p ∈ (1, ∞) the second continuous bounded cohomology group H²_cb(G, L^p(G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X). Partially supported by Sonderforschungsbereich 611.     

Hyperbolic Systems in Gelfand and Shilov Spaces

Ukrainian Mathematical Journal - For systems hyperbolic in Shilov’s sense whose coefficients are continuous functions of time, we study the properties of the Green function in S-type spaces....     

双曲复空间的拓扑结构与应用

双曲复空间与Minkowski空间相对应,具有时空方向异性的特点。以双曲复空间为原空间,可以抽象出一类双曲拟、虚度量空间和多拓扑结构。     

Geometry of Two- and Three-Dimensional Minkowski Spaces

A class of centrally-symmetric convex 12-topes (12-hedrons) in is described such that for an arbitrary prescribed norm on each polyhedron in the class can be inscribed in (circumscribed about) the -ball via an affine transformation, and this can be done with large degree of freedom. Bibliography: 5 titles.     

Eigenvalue Distributions and Geometry of Banach Spaces

We consider the sums Z⁽ⁿ⁾ of i.i.d. random vectors taking values in a d-dimensional Euclidean space. It is assumed that the so-called CRAMER condition holds in a neighbourhood of the origin. We establish lower bounds for the large deviation probabilities P(Z⁽ⁿ⁾ ? A) with A belonging to a large class of sets.     

Geometry of Configuration Spaces of Tensegrities

Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in ℝ ^d to admit a nonzero self-stress with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the configuration space of all n-tuples in ℝ ^d . In particular we find surgeries on graphs that give relations between different strata. Further we discuss questions related to geometric conditions defining the strata for plane tensegrities. We conclude the paper with particular examples of strata for tensegrities in the plane with a small number of vertices.     

Explicit Universal Deformations of Even Galois Representations

We investigate the case of deformations of even Galois representations. Our methods are the group theoretic ones mainly developed by Nigel Boston to study odd representations. We present conditions for Borel and tame cases under which the universal deformation ring is isomorphic to ?_p[[T]] and where we compute the universal deformation explicitly. Furthermore we produce a family of examples of totally real S₃ extensions which satisfy the above conditions in the tame case and we give examples in the Borel case. Finally we study the change of the deformation space under enlarging the ramification and thus give an example of an even representation that is not twist-finite.     

Nielsen Methods and Groups Acting on Hyperbolic Spaces

We show that for any n & in there exists a constant C(n) such that any n-generated group G which acts by isometries on a -hyperbolic space (with >0) is either free or has a nontrivial element with translation length at most C(n).     

Classification and Constructions of Complete Caps in Binary Spaces

We give new recursive constructions of complete caps in PG(n,2). We approach the problem of constructing caps with low dependency via the doubling construction and comparison to lower bounds. We report results of the exhaustive classification (up to projective equivalence) of all caps in PG(n,2) for n≤ 6. Research partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)     

关于复Banach空间的几何学

本文介绍复Ｂａｎａｃｈ空间几何学近年来的发展状况及其与向量值调和分析、Ｂ值鞅理论的联系。文章包括以下内容：１．几个反例；２．复凸性与复凸模；３．解析Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的分析特征；４．解析Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的几何特征；５．几种ＲＮ性质的比较；６．ＰＬ一致凸性的鞅刻画；７．Ｈ一致凸性的鞅刻画；８．向量值Ｈａｒｄｙ与Ｐａｌｅｙ不等式；９．解析ＵＭＤ空间。     

The Horospherical Geometry of Submanifolds in Hyperbolic Space

Some geometrical properties associated to the contact of submanifoldswith hyperhorospheres in hyperbolic n-space are studied as anapplication of the theory of Legendrian singularities.