Polynomial Convexity of Teichmuller Spaces

It is well known that finite-dimensional Teichmüller spacesare holomorphically convex, that is, they are domains of holomorphy.Moreover, the holomorphic convexity is fulfilled for all Teichmüllerspaces in a stronger form: they are complex hyperconvex. In this note we establish that, in fact, finite-dimensionalTeichmüller spaces possess a much stronger convexity property,namely, they are polynomially convex; in other words, they areRunge domains. Additionally, some geometric properties of Teichmüllerspaces are established.     

Tiling Infinite-Dimensional Normed Spaces

The present paper deals with real infinite-dimensional normedspaces; some of the main concepts here make sense, and havebeen treated in the literature, in the general context of topologicalHausdorff linear spaces over reals. A subset of a normed space X is a body if it is different fromX itself and is the closure of its non-empty interior. A coveringof X by bodies is called a tiling of X whenever any two differentmembers of it have disjoint interiors. The elements of sucha covering are called tiles. A tiling is bounded (respectivelyconvex) whenever each tile is bounded (respectively convex).1991 Mathematics Subject Classification 46B20.     

无限维空间中的实零点定理

在本文中，我们建立了无限维空间中的实零点定理，同时从仿射空间的拓扑结构和域的序结构两个方面，分别刻划了适合无限维实零点定理的序域．此外，本文有例子表明，对任意的基数α，确实存在适合α维实零点定理的序域．     

Teichmuller空间的星形结构问题

对于任一保持单位圆盘Δ及其外部Δ的Ｆｕｃｈｓ群Γ，利用Ｂｅｒｓ嵌入，Ｔｅｉｃｈｍｕｌｌｅｒ空间Ｔ（Γ）可看成是Δ上Γ的有界全纯二次微分Ｂ（Δ，Γ）中的一个有界区域，本文的目的是讨论Ｔｅｉｃｈｍｕｌｌｅｒ空间Ｔ（Γ）的星形问题。特别地，我们证明了：当Γ是第二类Ｆｕｃｈｓ群时，Ｔ（Γ）不是星形的．     

Infinite-Dimensional Measure Spaces and Frame Analysis

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ?, we study three cases of measures. We first show that, for ? infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ?. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.     

Distributions and Analytical Measures on Infinite-Dimensional Spaces

Spaces of test functions and spaces of distributions (generalized measures) on infinite-dimensional spaces are constructed, which, in the finite-dimensional case, coincide with classical spaces \(\mathscr{D}\) and \(\mathscr{D}'\). These distribution spaces contain generalized Feynman measures (but do not contain a generalized Lebesgue measure, which is not considered in this paper). For broad classes of infinite-dimensional differential equations in distribution spaces, the Cauchy problem has fundamental solutions. These results are much more definitive than those of A.Yu. Khrennikov’s and A.V. Uglanov’s pioneering works.     

Generalized Quasi-Variational Inequalities in Infinite-Dimensional Normed Spaces

In this paper, we deal with the following problem: given a real normed space E with topological dual E*, a closed convex set XE, two multifunctions :X2^X and , find such that We extend to the above problem a result established by Ricceri for the case (x)X, where in particular the multifunction is required only to satisfy the following very general assumption: each set (x) is nonempty, convex, and weakly-star compact, and for each yX–:X the set is compactly closed. Our result also gives a partial affirmative answer to a conjecture raised by Ricceri himself.     

A Fixed Point Theorem in Infinite-Dimensional Spaces

A generalization of the theorem of Miranda is given. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear Transformations of Smooth Measures on Infinite-Dimensional Spaces

We investigate the properties of the image of a differentiable measure on an infinitely-dimensional Banach space under nonlinear transformations of the space. We prove a general result concerning the absolute continuity of this image with respect to the initial measure and obtain a formula for density similar to the Ramer–Kusuoka formula for the transformations of the Gaussian measure. We prove the absolute continuity of the image for classes of transformations that possess additional structural properties, namely, for adapted and monotone transformations, as well as for transformations generated by a differential flow. The latter are used for the realization of the method of characteristics for the solution of infinite-dimensional first-order partial differential equations and linear equations with an extended stochastic integral with respect to the given measure.     

Partitioning Infinite-Dimensional Spaces for Generalized Riemann Integration

To form Riemann sums for generalized Riemann integrals, thedomain of integration must be partitioned in a suitable manner.The existence of the required partitions is usually proved bya simple method of repeated bisection of the domain of integration.However, when the domain is the Cartesian product of infinitelymany copies of the set of real numbers, this simple method ofproof has frequently failed. A proof which works for infinite-dimensionalspaces is provided here. 2000 Mathematics Subject Classification28C20.     

Localization for Hyperbolic Measures on Infinite-Dimensional Spaces

Functional Analysis and Its Applications - Properties of the extreme points of families of concave measures on infinite-dimensional locally convex spaces are studied. The localization method is...     

The Bers-Greenberg Theorem and the Maskit Embedding for Teichmuller Spaces

The Bers–Greenberg theorem tells us that the Teichmüllerspace of a Riemann surface with branch points (orbifold) dependsonly on the genus and the number of special points, and noton the particular ramification values. On the other hand, theMaskit embedding provides a mapping from the Teichmüllerspace of an orbifold, into the product of one-dimensional Teichmüllerspaces. In this paper we prove that there is a set of isomorphismsbetween one-dimensional Teichmüller spaces that, when restrictedto the image of the Teichmüller space of an orbifold underthe Maskit embedding, provides the Bers–Greenberg isomorphism.     

A Sufficient Condition for Rigidity in Extremality of Teichmuller Equivalence Classes by Schwarzian Derivative

The Strebel point is a TeichmOller equivalence class in the Teichmuller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmuller equivalence class of the universal Teichmuller space under which the class is a Strebel point. As an application, we construct a Teichmuller equivalence class that is a Strebel point and that is not an asymptotically conformal class.     

无穷维欧氏空间中球体及球面的Lebesgue测度

本分别给出了使在无穷维欧氏空间中球体和球面具有有限的,但又不是无穷小的测度的半径集合。     

Almost Frechet Differentiability of Lipschitz Mappings Between Infinite-Dimensional Banach Spaces

We give several sufficient conditions on a pair of Banach spacesX and Y under which each Lipschitz mapping from a domain inX to Y has, for every > 0, a point of -Fréchet differentiability.Most of these conditions are stated in terms of the moduli ofasymptotic smoothness and convexity, notions which have appearedin the literature under a variety of names. We prove, for example,that for > r > p 1, every Lipschitz mapping from a domainin an l_r-sum of finite-dimensional spaces into an l_p-sum offinite-dimensional spaces has, for every > 0, a point of-Fréchet differentiability, and that every Lipschitzmapping from an asymptotically uniformly smooth space to a finite-dimensionalspace has such points. The latter result improves, with a simplerproof, an earlier result of the second and third authors. Wealso survey some of the known results on the notions of asymptoticsmoothness and convexity, prove some new properties, and presentsome new proofs of existing results. 2000 Mathematical Subject Classification: 46G05, 46T20.     

Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces

This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypotheses of stability, convexity, and directional compactness. Counterexamples show that the hypotheses are minimal.