Generalized doubling constructions for constant mean curvature hypersurfaces in <Emphasis Type="Italic">S</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis>+1</Superscript>

The sphere S ⁿ⁺¹ contains a simple family of constant mean curvature (CMC) hypersurfaces of the form C _t : = S ^p (cos t) × S ^q (sin t) for p + q = n and called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges at a sufficiently symmetric configuration of points can be constructed by perturbative PDE methods. That is, one can create an approximate solution by gluing a rescaled catenoid into the neighbourhood of each point; and then one can show that a perturbation of this approximate hypersurface exists, which satisfies the CMC condition. The results of this paper generalize those of the authors in [3].     

Blaschke isoparametric hypersurfaces in the conformal space ℚ 1 n+1 , I

Let x : M → Q₁ⁿ⁺¹ be a regular hypersurface in the conformal space Q₁ⁿ⁺¹. We classify all the space-like Blaschke isoparametric hypersurfaces with two distinct Blaschke eigenvalues in the conformal space up to the conformal equivalence.     

n维Anti-de Sitter空间中类空超曲面的类时Gauss像的奇点

本文利用奇点理论研究了n维Anti-deSitter空间中的类空超曲面,介绍了类空超曲面的局部微分几何,定义了类时Anti-deSitterGauss像及Anti-deSitter高度函数,并进一步的利用Anti-deSitter高度函数族和流形间的切触理论研究了类时Anti-deSitterGauss像的几何意义及类空超曲面的通有性.最后研究了类空超曲面的AdS-Monge型.     

Finite-volume hyperbolic 4-manifolds that share a fundamental polyhedron

It is known that the volume function for hyperbolic manifolds of dimension 3 is finite-to-one. We show that the number of nonhomeomorphic hyperbolic 4-manifolds with the same volume can be made arbitrarily large. This is done by constructing a sequence of finite-sided finite-volume polyhedra with side-pairings that yield manifolds. In fact, we show that arbitrarily many nonhomeomorphic hyperbolic 4-manifolds may share a fundamental polyhedron. As a by-product of our examples, we also show in a constructive way that the set of volumes of hyperbolic 4-manifolds contains the set of even integral multiples of 4π²/3. This is “half” the set of possible values for volumes, which is the integral multiples of 4π²/3 due to the Gauss-Bonnet formula Vol(M) = 4π²/3 · χ(M).     

球面2型超曲面

本文在无先念条件下,证明了Ｃｈｅｎ［１］关于２型超曲面的一个定理．     

de Sitter空间中具有常均曲率的类空超曲面

设M是deSitter空间中具有常均曲率的类空超曲面,本文给出M是全脐的或是等参的一些条件．     

A NOTE ON THE QUADRILATERAL MESH CONDITION RDP（N,ψ）

The main aim of this paper is to show that the quadrilateral mesh condition RDP（N, ψ） is only sufficient but not necessary for the optimal order error estimate of the Q isoparametric element in the Hi norm.     

Meshfree isoparametric point interpolation method (IPIM) for evaporative laser drilling

An isoparametric point interpolation method (IPIM) has been developed to analyze evaporative laser machining. The method is based on isoparametric representation of the unknown in the local domain. It also uses a simple strong form, but shows to be powerful enough to handle highly localized boundary conditions. Solution in a typical influence domain is approximated by a polynomial function. The problem is geometrically nonlinear because the domain is not known a priori due to material removal in machining. An iterative scheme is introduced to solve the nonlinear problem. The material removal is handled by redistributing points in the domain. This renders the point distribution non-uniform same as random distribution. Three different boundary conditions considered are of essential, convection, and laser irradiation type. The numerical results show very good agreement with those by FEM and BEM.     

单位球面Sn+1(1)中具有常平均曲率的超曲面

利用流形的紧致性,研究了单位球面Sn+1(1)中具有常平均曲率的紧致超曲面上的Schrodinger算子,讨论了此算子的最小特征值与子流形结构之间的联系,并得到了相应的定理,证明过程比相关文献更简单.     

The cubic Segre variety in PG(5, 2)

The Segre variety in PG(5, 2) is a 21-set of points which is shown to have a cubic equation Q(x) = 0. If T(x, y, z) denotes the alternating trilinear form obtained by completely polarizing the cubic polynomial Q, then the associate U ^# of an r-flat is defined to be