In fact, the mean curvature and Gauss curvature of any helicoidal surface are independent on rotation parameter.
事实上，三维Minkowski空间中任意螺旋面的平均曲率和Gauss曲率都与旋转参数无关。
Thus, combining this work with Benekis work, we prove that there exist any type of helicoidal surface with mean curvature or Gauss curvature being any smooth function.
这样结合Beneki等人的工作，本文证明：三维Minkowski空间中，平均曲率或Gauss曲率为任意给定光滑函数的任意一类螺旋面都是存在的，并给出了具体的参数表达式。
In this paper, the Galerkin method is used to solve the Laplace-Young equation for calculation of simplified monodisperse emulsion system to obtain the relationship among mean curvature, contact angle, volume fraction, fractional fil...
获得了平均曲率、接触角、体积分数、接触面积分数、单位体积界面积等参数之间的关系，并提出了接触角不为零时的渗透压表达式。
And obtain that compact submanifolds with parallel mean curvature vector must be totally geodesic.
以及具有平行平均曲率向量的紧致子流形的全测性质。
We prove that the compact hypersurfaces and the hypersurfaces with constant mean curvature must be totally geodesic.
紧致超曲面以及常平均曲率超曲面的全测地性质。
The representation of the momentum operators differs from each other in these two kinds of coordinates, the former ones depend on the intrinsic geometrical quantities, but the latter case depend on a geometrical invariant, namely the mean curvature.
在量子力学中，动量和动能算符的表示在这两种描述中各有不同，前者的动量算符仅包含内禀几何量，后者的动量算符包含了曲面的平均曲率。
The Pinching problems are discussed on the sectional curvature of compact space-like pseudo-umbilical submanifolds M~n with parallel mean curvature vector in De Sitter space S~_p, and the theory of reduction of the codimension is obtained in De Sitter space through evaluating the Laplacian of square of the length.
讨论了De Sitter空间Snp+p中，具有平行平均曲率向量的紧致类空伪脐子流形Mn的截面曲率的拼挤问题，通过估计第二基本形式模长平方的Laplacian，得到了De Sitter空间中的余维数压缩定理。
Some uniform formulae are established, which link the Laplacian of the position vector function to the mean curvature vector field on any submanifold in the space forms.
讨论空间型中的位置向量场，建立一组统一的公式，将子流形的平均曲率向量场与位置向量及其衍生函数的Laplacian联系在一起。
Triangular mesh, normal vector, principal curvature, gaussian curvature, mean curvature
三角网格，法向量，主曲率，高斯曲率，平均曲率
Let be a compact pseudo-umbilical submanifolds with parallel mean curvature vector in the quasi constant curvature space.
设Mn是拟常曲率空间Nn+p中具有平行平均曲率向量的紧致伪脐子流形，论证得到了这种子流形的两个内蕴积分不等式，从而给出了Mn是全脐子流形的两个内蕴充分条件。
In this thesis, we totally depict the spectrum of the Laplacian on theclosed hypersurface with constant mean curvature and constant scalar curvaturein S~4, i. e., compute all eigenvalues of such closed hypersurface.
本文完整地刻画了S~4中具有常平均曲率和常数量曲率的闭超曲面上Laplace算子的谱，即计算出这类闭超曲面的各阶特征值。
In this article, we mainly study the space-like submanifolds with parallel mean curva-ture vector, constant scalar curvature or constant square length of the second fundamental form, respectively. We obtain some pinching theorems and rigidity results by estimating Laplace of the square length of the second fundamental form of the such submanifolds and using yaus maximum principle or Stokes Theorem.
本论文主要研究de Sitter空间中具有平行平均曲率向量、常数量曲率或第二基本形式模长平方是常数的三类类空子流形，并通过分别估计三种情形下子流形的第二基本形式模长平方的Laplace，利用Yau的极大值原理和Stokes定理，获得了这些子流形的一些拼挤定理和刚性定理。
We then introduce a conformal invariant quantity which is formulated in terms of the square of the length of the trace free part of the second fundamental form and the mean curvature, and prove that if this quantity is bounded above by that value of the Clifford torus then x is either a totally umbilical sphereor a conformal Clifford torus.
接著我们介绍一个由第二基本型式迹为零部份的张量长度平方与平均曲率形成的保角不变量，并证明此保角不变量的上界若为Clifford环面之值，则x不是全脐球面就是Clifford环面的保角类。
Let x be an immersion of a compact Willmore surface M into the n-dimensional unit sphere Sn. In this thesis we first consider the Willmore surfaces in the unit 3-sphere, and establish an integral inequality for the square of the length of the trace free part of the second fundamental form and the mean curvature.
令x是一个从紧致威尔摩曲面M到n 维单位球面Sn的浸入，在本论文中我们首先考虑3维单位球面中的威尔摩曲面并建立一个包含第二基本型式迹为零部份的张量长度平方与平均曲率之积分不等式。
See [1] and obtain the following: Theorem 1.1 The only immersed compact spacelike hypersurfaces with constant mean curvature in Ln+l spanning a sphere Sn-1 are Bn or...
为边界的紧致常平均曲率类空超曲面，则M只有n维圆盘B~n和超伪球面盖。
See [1] and obtain the following:Theorem 1.1 The only immersed compact spacelike hypersurfaces with constant mean curvature in Ln+l spanning a sphere Sn-1 are Bn or hyperbolic cap...
为边界的紧致常平均曲率类空超曲面，则M只有n维圆盘B~n和超伪球面盖。关于R~(n+1)中常平均曲率超曲面的相应问题至今尚未解决。
This dissertation is devoted to the global existence and quench ing phenomena of the solution to a nonlinear parabolic equation of the mean curvature type and the blow-up conditions to another nonlinear parabolic equation.
本文研究了一类平均曲率型抛物方程解的整体存在性和解的熄灭现象及一类非线性抛物方程解的爆破条件。
Global existence and quench ing phenomena for a parabolic equation of the mean curvature type with nonlinear convection term
若初值u0∈Lq，q≥n，问题的解将在有限时刻熄灭，并且给出了解的L∞估计。
Submanifold; Homology group; Topological sphere theorem; L~2 harmonic 1-forms; Ends; Eigenvalue; Mean curvature; Second fundamental form
基础科学，数学，几何、拓扑子流形；同调群；拓扑球面定理； L~2调和1-形式；端；特征值；平均曲率；第二基本形式
In this paper, we mainly study the gap of the second fundamental form of hypersurface with constant mean curvature in the unit sphere.
本文主要研究了单位球面内常平均曲率超曲面的第二基本形式模长平方的间隙性。