Complete Space-like λ-surfaces in the Minkowski Space R_1~3 with the Second Fundamental Form of Constant Length

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space R_1~3. As the result, we obtain a complete classification theorem for all the complete space-like λ-surfaces x : M~2→ R_1~3 with the second fundamental form of constant length. This is a natural extension to the λ-surfaces in R_1~3 of a recent interesting classification theorem by Cheng and Wei for λ-surfaces in the Euclidean space R~3.     

The moduli space of embedded singly periodic maximal surfaces with isolated singularities in the Lorentz–Minkowski space $$\mathbb{L}^3$$

We show that, up to some natural normalizations, the moduli space of singly periodic complete embedded maximal surfaces in the Lorentz–Minkowski space , with fundamental piece having a finite number (n + 1) of singularities, is a real analytic manifold of dimension 3n + 4. The underlying topology agrees with the topology of uniform convergence of graphs on compact subsets of {x ₃ = 0}.      

The Best Constant in the Embedding of WN,1(ℝN) into L ∞ ( ℝ N ) $L^{\infty }(\mathbb {R} ^{N})$

Potential Analysis - We compute the best constant in the embedding of $W^{N,1}(\mathbb {R} ^{N})$ into $L^{\infty }(\mathbb {R} ^{N})$ , extending a result of Humbert and Nazaret in dimensions one...     

E1^3中类空曲面上的一类直线汇

研究了三维Minkowski空间E1^3中,类空曲面上曲率线族的切线构成的双曲型直线汇.不仅推广了Abdel-Baky^[1,2]的结论,还进一步研究了此类线汇在E1^3中的其它性质.     

不定复空间型中具有平行平均曲率向量的完备全实类空子流形

利用活动标架法和广义极大值原理研究了不定复射影空间中完备的具有平行平均曲率向量的全实类空子流形,得到这类子流形的Pinching定理.     

局部对称Lorentz空间中的具有常数量曲率的完备类空超曲面

The complete space-like hypersurfaces with constant normal saclar curvature is discussed in a locally symmetric Lorentz space. A classified theorem is obtained by the operator L_1 introduced by S Y Cheng and S T Yau [3].     

The Gauss Map and Second Fundamental Form of Surfaces in \mathbb{R}^3

Given a surface S, a map N from S to and a conformal structure on S, we solve the problem of the existence and uniqueness of an immersion with a Gauss map N such that the conformal structure on S is the induced by the second fundamental form.     

共形空间中平行的共形第二基本形式的类空超曲面

研究Lorentz空间形式中的共形几何,并对共形空间中的平行的共形第二基本形式的类空超曲面进行了分类.     

共形空间中具有平行的共形第二基本形式的I型类时超曲面的分类

共形空间中具有平行的共形第二 基本形式的类空超曲面已经作了完全分类, 本文将继续类时情形的探讨并对此时的I型 类时超曲面分类.       

Immersed Hypersurfaces in the Unit Sphere S^m＋1 with Constant Blaschke Eigenvalues

For an immersed submanifold x ： M^m→ Sn in the unit sphere S^n without umbilics, an eigenvalue of the Blaschke tensor of x is called a Blaschke eigenvalue of x. It is interesting to determine all hypersurfaces in Sn with constant Blaschke eigenvalues. In this paper, we are able to classify all immersed hypersurfaces in S^m＋1 with vanishing MSbius form and constant Blaschke eigenvalues, in case （1） x has exact two distinct Blaschke eigenvalues, or （2） m = 3. With these classifications, some interesting examples are also presented.     

Complete minimal hypersurfaces in the hyperbolic space with vanishing Gauss-Kronecker curvature

We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with Gauss-Kronecker curvature identically zero, a nowhere vanishing second fundamental form and a scalar curvature bounded from below.