Ribaucour Transformations for Hypersurfaces in Space Forms

The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20.     

广义生灭最小Q过程的可配称性

研究全稳定广义生灭最小Q过程的可配称性,获得广义生灭最小Q过程是可配称的充分必要条件,以及最小Q过程是唯一的可配称Q过程的充分必要条件．     

Horizontal Connection and Horizontal Mean Curvature in Carnot Groups

In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.     

Estimates for the Eigenvalues of Matrices

For matrices whose eigenvalues are real (such as Hermitian or real symmetric matrices), we derive simple explicit estimates for the maximal (λ_max) and the minimal (λ_min) eigenvalues in terms of determinants of order less than 3. For 3 × 3 matrices, we derive sharper estimates, which use det A but do not require to solve cubic equations.     

Choquet-type Integral Representation of Invariant Functions for some Product Semigroups

We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions.     

Banach空间中二阶积分-微分方程的初值问题

使用锥理论及单调迭代技术，首先讨论了Banach空间中一阶积分-微分方程初值问题的最小最大解的存在性，并在此基础上讨论了带有一阶微分项的二阶积分-微分方程初值问题的最小最大解的存在性。     

A minimal pair joining to a plus cupping Turing degree

A computably enumerable (c.e.) degree a is called nonbounding, if it bounds no minimal pair, and plus cupping, if every nonzero c.e. degree x below a is cuppable. Let NB and PC be the sets of all nonbounding and plus cupping c.e. degrees, respectively. Both NB and PC are well understood, but it has not been possible so far to distinguish between the two classes. In the present paper, we investigate the relationship between the classes NB and PC , and show that there exists a minimal pair which join to a plus cupping degree, so that PC ? NB . This gives a first known difference between NB and PC . (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Connecting orbits among Denjoy minimal sets for monotone twist map

In a Birkhoff region of instability for an exact area-preserving twist map, we construct some orbits connecting distinct Denjoy minimal sets. These sets correspond to the local, instead of global minimum of the Lagrangian action. In the earlier work, Mather constructed connecting orbits among Aubry-Mather sets and the global minimizer of the Lagrangian action.     

每个算子都是两个强不可约算子的和

本文证明了可分无穷维 Hilbert空间上每个有界线性算子均可写成两个强不可约算子之和 .这回答了文献 [9]中提出一个公开问题     

Weak Density of Smooth Maps in W 1, 1(M,N) for Non-Abelian π1(N)

We prove that smooth maps are dense in the sense of biting convergence in W ^{1, 1}(M, N) when M and Nare compact Riemannian manifolds and N is closed.