Necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators

Fibrators help detect approximate fibrations. A closed, connected -manifold is called a codimension-2 fibrator if each map defined on an -manifold such that all fibre , are shape equivalent to is an approximate fibration. The most natural objects to study are s-Hopfian manifolds. In this note we give some necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators.

     

关于Kellogg定理的若干推广

本文以连续模,光滑模为工具,讨论由单位圆至光滑的若当曲线Ｌ所范单连通区的保角映射问题,对于Ｋｅｌｌｏｇｇ定理作了较大幅度的推广,得出了新的结果。     

Generalized Big Picard Theorem for pseudo-holomorphic maps

We show how an appropriate choice for affine connections in the target manifold allows the pseudo-holomorphic curves to be realized as harmonic maps. As an application, we present a generalized Big Picard Theorem for pseudo-holomorphic maps between manifolds with almost complex structures.     

Holomorphic Symplectic Manifolds and Lagrangian Fibrations

We introduce the geometrical nature of fibre space structures of an irreducible symplectic manifold and holomorphic Lagrangian fibrations.     

广义KKM定理的推广

本文给出了更一般的广义 KKM定理 ,使定理更简洁 ,应用更广泛和方便     

A Callias-Type Index Theorem with Degenerate Potentials

A generalization of Callias’ index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. The index obtained depends on the choice of a family of Fredholm extensions, though as in the classical version it depends only on the data at infinity.     

Connected sums of manifolds which induce approximate fibrations

Codimension-2 fibrators are -manifolds which automatically induce approximate fibration, in the following sense: given any proper mapping from an -manifold onto a -manifold such that each point-preimage is a copy of the codimension-2 fibrator, is necessarily an approximate fibration. In this paper, we give some answers to the following question: given an -manifold which is a nontrivial connected sum, when is a codimension-2 fibrator?

     

关于极限定理的一个结果及其推广

给出了一个关于可列非齐次马尔可夫链M元状态序组出现频率的一个强极限定理及其推广,所得结论对任意可列非齐次马尔可夫链普遍成立.     

Families of Lagrangian fibrations on hyperkähler manifolds

A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known (due to Huybrechts) that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact, simple hyperkähler manifold with _b2?7$b_2?7$ admits only finitely many deformation types of holomorphic Lagrangian fibrations. We also prove that all known hyperkähler manifolds are never Kobayashi hyperbolic.     

A New Proof of Calabi-Yau＇s Theorem

We give a new proof of Calabi-Yau＇s theorem on the volume growth of Riemannian manifolds with non-negative Ricci curvature.     

A New Proof of Calabi-Yau's Theorem

We give a new proof of Calabi-Yau's theorem on the volume growth of Rie- mannian manifolds with non-negative Ricci curvature.     

关于Hutton定理的一个注

本文证明了存在一个一一对应$\varphi: {\cal J}\cup{\cal J}'\longrightarrow\delta\cup\delta'$,它满足: \ \ (1) $\varphi|{\cal J}: ({\cal J},\subset)\longrightarrow(\delta,\leq)$是frame同构. \ \ (2) $\varphi|{\cal J}': ({\cal J}',\subset)\longrightarrow(\delta',\leq)$是coframe同构.     

A Holomorphic Extension Theorem using Clifford Analysis

In this paper a new holomorphic extension theorem is presented using Clifford analysis.     

KKM定理的一个推广

本文引入了Z-空间概念,定义了一类新的映射：Z-KKM映射,推广了著名的FKKM定理及其它各种形式的KKM定理.     

Maps from a Simply Connected Space to Flag Manifold G／T

In this paper the classification of maps from a simply connected space X to a flag manifold G/T is studied. As an application, the structure of the homotopy set for self-maps of flag manifolds is determined.     

A Cylinder Theorem for Isometric Pluriharmonic Immersions

We prove a cylinder theorem for isometric pluriharmonic immersions of complete Kähler manifolds into semi-Euclidean spaces under an assumption concerning the index of relative nullity.     

半代数集的一个计数定理及其应用

给出半代数集基数的计数原理和不可约紧代数流形上Euler示性数及亏格的算法.     

集值映象重合点定理的进一步改进和推广

本文是文［１］的继续．在更一般的条件下，研究了完备度量空间中集值映象的重合点和不动点存在性问题