On the intrinsic complexity of point finding in real singular hypersurfaces

In previous work we designed an efficient procedure that finds an algebraic sample point for each connected component of a smooth real complete intersection variety. This procedure exploits geometric properties of generic polar varieties and its complexity is intrinsic with respect to the problem. In the present paper we introduce a natural construction that allows to tackle the case of a non-smooth real hypersurface by means of a reduction to a smooth complete intersection.     

等值面的生成原理与算法

本文从工程实际中引出,由四变量离散数据图示等值曲面的问题,提出了构造等值曲面的四维画法几何生成方法,在用计算机实现此生成方法的过程中,从理论上证明了1982年Nguyen-Van-Phai提出的四面体网格化算法,这种算法的性质,即四面体球面过剩为最大的情况下是最佳的,可以有效地应用于计算机绘图和有限元分析的网格自动生成等方面。本文用此算法求出四变量离散数据的等值点,从而实现等值曲面的拟合。     

洛伦兹空间型S1^n＋1中的Ⅱ型洛伦兹等参超曲面的Cartan恒等式

研究了洛伦兹空间型S1^n＋1中的Ⅱ型洛伦兹等参超曲面并证明了其主曲率的Cartan恒等式．     

关于常中曲率紧致超曲面的一个Pinching定理

讨论了具有常数曲率流形的常中曲率紧致超曲面 ,在某些Pinching条件下 ,得出该超曲面是全脐的 ,且等距于标准球面     

CHn中的等参超曲面

M是CHn中的等参超曲面,e是M上的单位法向量场,当J(e)是主向量时,证明了M的不同主曲率数只能是2或3;M=π-1(M)是H12n 1中的等参超曲面,不同的主曲率数是1,2,4.     

De sitter空间的2-调和类空子流形

研究了Ｄｅ ｓｉｔｔｅｒ空间Ｓｐ＾ｎ＋ｐ（１）的２－调和类空子流形的全测地性和关于第二基本形式长度平方的拼挤结果。     

Direct detection of flow discontinuities by 3D curvature operators

We present an approach for the direct detection of flow discontinuities which avoids explicit computation of a dense optic flow field. It is based on regarding the time varying image as a hypersurface in four-dimensional space and on using the Gaussian curvature properties of this hypersurface as a direct indicator for the presence of motion discontinuities. An easy to implement, nonlinear operator is suggested and possible extensions of the basic scheme are discussed.     

Interpolation of digital imagery using hypersurface approximation

An algorithm for interpolation by piece-wise polynomial approximation has been developed and implemented. The hypersurface approximation is carried out by a quadratic surface defined over a two dimensional space of the digital picture in the neighbourhood of the point to be interpolated using orthogonal polynomials as basis functions. The kernel for interpolation has been evaluated with the help of polynomial basis functions; this enables efficient implementation of the algorithm.     

关于极小嵌入超曲面第一特征值的一个注记

设N是Ricci曲率以正常数k为下界的n＋1维紧致定向黎曼流形,M是嵌入在N中的定向极小闭超曲面.本文给出M上Laplace算子的第一特征值λ1的新的下界估计,改进了已有结论,使之更接近于丘成桐关于该问题的猜想.     

局部对称共形平坦黎曼流形的2－调和超曲面

将单位球面中紧致２－调和超曲面关于第二基本形式长度平方的Ｐｉｎｃｈｉｎｇ结果推广到局部对称共形平坦黎曼流形中的紧致２－调和超曲面．