非紧致一秩Rienann对称空间上的中心极限定理

我们在本文中研究非紧致一秩Riemann对称空间上初等球函数的渐近表示,并利用LohoueN.和RychnerTh.得到的热核表达式,建立起这类空间上的非欧中心极限定理,所得结果包含了Terras的定理作为其特例.     

非紧致一秩Riemann对称空间上的中心极限定理

我们在本文中研究非紧致一秩Ｒｉｅｍａｎｎ对称空间上初等球函数的渐近表示,并利用Ｌｏｈｏｕｅ Ｎ．和Ｒｙｃｈｎｅｒ Ｔｈ．得到的热核表达式,建立起这类空间上的非欧中心极限定理,所得结果包含了Ｔｅｒｒａｓ的定理作为其特例．     

广义区间空间中参数型非紧KKM定理及其在经济平衡问题上的应用

在不具线性结构的拓扑空间———广义区间空间———中证明了集值映像参数型非紧的 KKM定理,用本文结果研究了极大极小问题和拓扑型广义经济Shafer Sonneischein平衡存在问题.     

Geometric quantization for proper moment maps

We establish a geometric quantization formula for Hamiltonian actions of a compact Lie group acting on a non-compact symplectic manifold such that the associated moment map is proper. In particular, we give a solution to a conjecture of Michèle Vergne. To cite this article: X. Ma, W. Zhang, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Sobolev Inequalities on Forms and <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis>,<Emphasis Type="Italic">q</Emphasis></Superscript>-Cohomology on Complete Riemannian Manifolds

We prove some Sobolev inequalities on differential forms over a class of complete non-compact Riemannian manifolds with suitable geometric conditions. Moreover, we establish some L ^p,q -estimates and existence theorems of the Cartan-De Rham equation and the Hodge systems. As applications, we prove some vanishing theorems of the L ^p,q -cohomology and prove the L ^q -solvability of the nonlinear p-Laplace equation on forms on complete non-compact Riemannian manifolds with suitable geometric conditions.     

A class of Kazdan-Warner typed equations on non-compact Riemannian manifolds

In this paper,we discuss a Kazdan-Warner typed equation on certain non-compact Rie- mannian manifolds.As an application,we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles over certain non-compact K(?)hler manifolds.     

On the connected component of compact composition operators on the Hardy space

We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space H². This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols. As a main tool we use Aleksandrov-Clark measures.     

Harmonic manifolds with minimal horospheres

For a non-compact harmonic manifold M, we establish an integral formula for the derivative of a harmonic function on M. As an application we show that for the harmonic spaces having minimal horospheres, bounded harmonic functions are constant. The main result of this article states that the harmonic spaces having polynomial volume growth are flat. In other words, if the volume density function Θ of M has polynomial growth, then M is flat. This partially answers a question of Szabo namely, which density functions determine the metric of a harmonic manifold. Finally, we give some natural conditions which ensure polynomial growth of the volume function.     

Isometry Groups and Geodesic Foliations of Lorentz Manifolds. Part I: Foundations of Lorentz Dynamics

This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present part we investigate the dynamics of affine, and especially Lorentz transformations. In particular we show how this is related to geodesic foliations. The existence of geodesic foliations was (very succinctly) mentioned for the first time by D'Ambra and Gromov, who suggested that this may help in the classification of compact Lorentz manifolds with non-compact isometry groups. In the Part II of the series, a partial classification of compact Lorentz manifolds with non-compact isometry group will be achieved with the aid of geometrical tools along with the dynamical ones presented here. Submitted: October 1997, revised: November 1998.     

Non-compact $$\text {RCD}(0,N)$$ Spaces with Linear Volume Growth

Since non-compact \(\text {RCD}(0, N)\) spaces have at least linear volume growth, we study non-compact \(\text {RCD}(0,N)\) spaces with linear volume growth in this paper. One of the main results is that the diameter of level sets of a Busemann function grows at most linearly on a non-compact \(\text {RCD}(0,N)\) space satisfying the linear volume growth condition. Another main result in this paper is a rigidity theorem at the non-compact end for a \(\text {RCD}(0,N)\) space with strongly minimal volume growth. These results generalize some theorems on non-compact manifolds with non-negative Ricci curvature to non-smooth settings.     

Semilinear subelliptic problems without compactness on Lie groups

An abstract version of concentration compactness on Hilbert spaces applies to to actions of non-compact Lie groups. Using the concentration compactness argument we prove existence of solutions for semilinear problems involving sub-Laplacians on the whole Lie group and on their cer-tain non-compact subsets, including minimizers for Sobolev inequalities. The result is stated for any real connected finite-dimensional Lie group.     

The number of critical elements of discrete Morse functions on non-compact surfaces

This paper is focused on looking for links between the topology of a connected and non-compact surface with finitely many ends and any proper discrete Morse function which can be defined on it. More precisely, we study the non-compact surfaces which admit a proper discrete Morse function with a given number of critical elements. In particular, given any of these surfaces, we obtain an optimal discrete Morse function on it, that is, with the minimum possible number of critical elements.     

Generalized Bergman kernels on symplectic manifolds

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As a consequence, we calculate the density of states function of the Bochner-Laplacian and establish a symplectic version of the convergence of the induced Fubini-Study metric. We also discuss generalizations of the asymptotic expansion for non-compact or singular manifolds as well as their applications. Our approach is inspired by the analytic localization techniques of Bismut and Lebeau.     

Fixed Point Theorems for Non-convex Valued Multifunctions

The purpose of this paper is to establish fixed point theorems for non-convex valued multifunctions which generalize known results in the literature. We also derive coincidence theorems in the non-compact setting.AMS Subject Classification (2000): 47H, 54H     

集值映射的Nash平衡点的存在定理

本文引入了集值映射的Nash平衡点的概念，它以通常的Nash平衡点及Loose Nash平衡点为特例，并在紧和非紧的假设下，得到集值映射的Nash平衡点的存在定理，其中在非紧的情况下使用escaping序列的定义．     

Homotopic properties of confluent maps in the proper category

We establish some properties of homotopical nature for confluent maps in the proper category. We analyze in this setting the characterization of tree-like continua by J.H. Case and R.E. Chamberlin as well as the theorem by T.B. McLean on the preservation of tree-likeness under confluent maps. We give counterexamples for the corresponding proper analogues and we extend results of several authors in classical continuum theory to non-compact spaces. Finally, we describe the behavior of these maps with respect to the fundamental pro-group, generalizing results of J. Grispolakis and other authors. Two questions of interest are still open (Open Question 15 and Conjecture 24).     

Twisted holomorphic chains and vortex equations over non-compact Kähler manifolds

In this paper, we study twisted holomorphic chains and related gauge equations over non-compact Kähler manifolds. We use the heat flow method to solve the Dirichlet boundary problem for the related gauge equations, and prove a Hitchin-Kobayashi type correspondence for twisted holomorphic chain over some non-compact Kähler manifolds.     

The Geometry of the Newton Method on Non-Compact Lie Groups

An important class of optimization problems involve minimizing a cost function on a Lie group. In the case where the Lie group is non-compact there is no natural choice of a Riemannian metric and it is not possible to apply recent results on the optimization of functions on Riemannian manifolds. In this paper the invariant structure of a Lie group is exploited to provide a strong interpretation of a Newton iteration on a general Lie group. The paper unifies several previous algorithms proposed in the literature in a single theoretical framework. Local asymptotic quadratic convergence is proved for the algorithms considered.     

Constancy of p-harmonic maps of finite q-energy into non-positively curved manifolds

We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively curved target. First, we establish a uniqueness result for the p-harmonic representative in the homotopy class of a constant map. Next, we derive a Caccioppoli inequality for the energy density of a p-harmonic map and we prove a companion Liouville type theorem, provided the domain manifold supports a Sobolev–Poincaré inequality. Finally, we obtain energy estimates for a p-harmonic map converging, with a certain speed, to a given point.