Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings

In this paper we shall show that the boundary of the hyperbolic building considered by M. Bourdon admits Poincaré type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of and the fact that every quasiconformal homeomorphism is quasisymmetric. Therefore by these results, the answer to questions 19 and 20 of Heinonen and Semmes (Thirty-three YES or NO questions about mappings, measures and metrics, Conform Geom. Dyn. 1 (1997), 1-12) is NO.

     

Normality criteria for families of holomorphic mappings of several complex variables into

By applying the heuristic principle in several complex variables obtained by Aladro and Krantz, we shall prove some normality criteria for families of holomorphic mappings of several complex variables into , the complex N-dimensional projective space, related to Green's and Nochka's Picard type theorems. The equivalence of normality to being uniformly Montel at a point will be obtained. Some examples will be given to complement our theory in this paper.

     

On a Primal-Dual Analytic Center Cutting Plane Method for Variational Inequalities

We present an algorithm for variational inequalities VI( , Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the definition of the set Y are taken explicitly into account.We report numerical experiments on several well—known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one.     

Fuzzy度量空间中映像族的公共不动点定理

本文讨论了Fuzzy度量空间中映像对和映像族的公共不动点问题,所获定理推广了Kaleva.O Seikkala. S和郑叔的有关结果。     

A Derivative-Coderivative Inclusion in Second-Order Nonsmooth Analysis

For twice smooth functions, the symmetry of the matrix of second partial derivatives is automatic and can be seen as the symmetry of the Jacobian matrix of the gradient mapping. For nonsmooth functions, possibly even extended-real-valued, the gradient mapping can be replaced by a subgradient mapping, and generalized second derivative objects can then be introduced through graphical differentiation of this mapping, but the question of what analog of symmetry might persist has remained open. An answer is provided here in terms of a derivative-coderivative inclusion.     

Convergence Groups, Hausdorff Dimension, and a Theorem of Sullivan and Tukia

We show that a discrete, quasiconformal group preserving ⁿ has the property that its exponent of convergence and the Hausdorff dimension of its limit set detect the existence of a non-empty regular set on the sphere at infinity to ⁿ . This generalizes a result due separately to Sullivan and Tukia, in which it is further assumed that the group act isometrically on ⁿ , i.e. is a Kleinian group. From this generalization we are able to extract geometric information about infinite-index subgroups within certain of these groups.     

On the Existence of Solutions of Quasivariational Inclusion Problems

Quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of general vector ideal, proper, Pareto, weak quasioptimization problems, quasivariational inequalities, and vector quasiequilibrium problems. Further, we prove theorems on the existence for solutions of systems of these inclusions. As a corollary, we obtain an ideal minimax theorem concerning vector functions.     

Convergence of harmonic maps on the Poincaré disk

Let be a sequence of locally quasiconformal harmonic maps on the unit disk with respect to the Poincaré metric. Suppose that the energy densities of are uniformly bounded from below by a positive constant and locally uniformly bounded from above. Then there is a subsequence of that locally uniformly converges on , and the limit function is either a locally quasiconformal harmonic map of the Poincaré disk or a constant. Especially, if the limit function is not a constant, the subsequence can be chosen to satisfy some stronger conditions. As an application, it is proved that every point of the space , a subspace of the universal Teichmüller space, can be represented by a quasiconformal harmonic map that is an asymptotic hyperbolic isometry.

     

Fixed points of asymptotic contractions

Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies