共查询到20条相似文献,搜索用时 15 毫秒
1.
Qiaoling Wang 《Monatshefte für Mathematik》2003,84(1):163-167
In this paper, we prove some rigidity theorems for Clifford minimal hypersurfaces in a unit sphere. 相似文献
2.
Qiaoling Wang 《Monatshefte für Mathematik》2003,140(2):163-167
In this paper, we prove some rigidity theorems for Clifford minimal hypersurfaces in a unit sphere.Received March 18, 2002; in revised form December 25, 2002
Published online October 15, 2003 相似文献
3.
SUN Jun 《偏微分方程(英文版)》2009,22(4):352-361
In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 (1982), pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method. 相似文献
4.
Zhou Zhenrong 《东北数学》1997,(1)
SpectralCharacterizationsofClifordMinimalHypersurfacesZhouZhenrong(周振荣)(WuhanFoodIndustryColege,Wuhan,430022)AbstractInthispa... 相似文献
5.
Marian Ioan Munteanu Oscar Palmas Gabriel Ruiz-Hernández 《Mediterranean Journal of Mathematics》2016,13(5):2659-2676
The graph of a function f defined in some open set of the Euclidean space of dimension (p + q) is said to be a translation graph if f may be expressed as the sum of two independent functions ? and ψ defined in open sets of the Euclidean spaces of dimension p and q, respectively. We obtain a useful expression for the mean curvature of the graph of f in terms of the Laplacian, the gradient of ? and ψ as well as of the mean curvatures of their graphs. We study translation graphs having zero mean curvature, that is, minimal translation graphs, by imposing natural conditions on ? and ψ, like harmonicity, minimality and eikonality (constant norm of the gradient), giving several examples as well as characterization results. 相似文献
6.
Thomas Hasanis Andreas Savas-Halilaj Theodoros Vlachos 《Monatshefte für Mathematik》2005,145(4):301-305
In this paper we investigate complete minimal hypersurfaces
with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(Mn) is a minimal Clifford torus. 相似文献
7.
Thomas Hasanis Andreas Savas-Halilaj Theodoros Vlachos 《Monatshefte für Mathematik》2005,71(1):301-305
In this paper we investigate complete minimal hypersurfaces
f : Mn? \Bbb Sn+1f : M^{n}\rightarrow {\Bbb S}^{n+1}
with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(Mn) is a minimal Clifford torus. 相似文献
8.
Minimal Determinants and Lattice Inequalities 总被引:1,自引:0,他引:1
Some results of P. McMullen on determinants of sublattices ofZd induced by rational subspaces are generalized to arbitrarylattices. As an application, we obtain an equality for the minimaldeterminants introduced by J. M. Wills, namely Dt(L) = Dd(L)Dd1((L*).Using an inequality of Lagarias, Lenstra and Schnorr, we generalizetwo isoperimetric inequalities withlattice constraints by Bokowski,Hadwiger and Wills, and Hadwiger, respectively, to arbitrarylattices. 相似文献
9.
The existence and uniqueness theorem for isotropic hypersurfaces with prescribed boundary in Lorentzian warped products is
proved.The proof is based on minimal Lipschitz extensions of functions.
__________
Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 39, No. 3, pp. 28–36, 2005
Original Russian Text Copyright #x00A9; by A. A. Klyachin and V. M. Miklyukov 相似文献
10.
Andreas Savas-Halilaj 《Journal of Geometric Analysis》2013,23(3):1032-1057
The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss–Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with vanishing Gauss–Kronecker curvature and scalar curvature bounded from below. 相似文献
11.
本文的研究分为两部分.第一部分是在特殊的Randers空间中得到了等距浸入的HT-极小旋转超曲面,这些特殊的Rander空间是非Minkowski的,但是它们的旗曲率为零.第二部分刻画了Funk空间中的各向异性极小旋转超曲面. 相似文献
12.
本文证明了双曲空间中的共形平坦极小超曲面必为旋转超曲面或由一些旋转超曲面片用全测地超曲面片粘合而成.将这结果与王新民及许志才的一个已发表定理相组合,推广了Blair关于推广悬链面的一个定理. 相似文献
13.
14.
Michael Brunnbauer 《Geometric And Functional Analysis》2008,18(4):1087-1117
We show that the systolic constant, the minimal volume entropy, and the spherical volume of a manifold depend only on the
image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant
of manifolds with fundamental group of order two (modulo the value for the real projective space) and derive an inequality
between the minimal volume entropy and the systolic constant.
Received: February 2007, Revised: November 2007, Accepted: December 2007 相似文献
15.
16.
Egon Balas 《Computational Optimization and Applications》1998,10(2):189-193
Projection of a polyhedron involves the use of a cone whose extreme rays induce the inequalities defining the projection. These inequalities need not be facet defining. We introduce a transformation that produces a cone whose extreme rays induce facets of the projection. 相似文献
17.
Qing Chen 《Annals of Global Analysis and Geometry》2001,19(2):177-184
We obtain curvature estimates for certain stable minimalhypersurfaces in R
4 and R
5without using volume bounds. It follows that if M is acomplete stable minimal hypersurface in R
4 orR
5, then M is a hyperplane whenM intersects each extrinsic ball in, at most,N-components. 相似文献
18.
Yong Luo 《Results in Mathematics》2014,65(1-2):49-56
A submanifold M m of a Euclidean space R m+p is said to have harmonic mean curvature vector field if ${\Delta \vec{H}=0}$ , where ${\vec{H}}$ is the mean curvature vector field of ${M\hookrightarrow R^{m+p}}$ and Δ is the rough Laplacian on M. There is a famous conjecture named after Bangyen Chen which states that submanifolds of Euclidean spaces with harmonic mean curvature vector fields are minimal. In this paper we prove that weakly convex hypersurfaces (i.e. hypersurfaces whose principle curvatures are nonnegative) with harmonic mean curvature vector fields in Euclidean spaces are minimal. Furthermore we prove that weakly convex biharmonic hypersurfaces in nonpositively curved space forms are minimal. 相似文献
19.
Isoperimetric Inequalities for Extrinsic Balls in Minimal Submanifolds and their Applications 总被引:3,自引:0,他引:3
S.-Y. Cheng, P. Li and S.-T. Yau proved comparison theoremsfor the volume of extrinsic balls in minimal submanifolds ofspace forms. These results were extended by S. Markvorsen forminimal submanifolds of a riemannian manifold with just an upperbound on the sectional curvature. In the paper an isoperimetricinequality for extrinsic balls in minimal submanifolds of ariemannian manifold N with sectional curvatures bounded fromabove by a non-positive constant is found. As a corollary ofthis result an alternative proof is obtained of the comparisonfor the volume of extrinsic balls stated by the preceding authors,but now the equality case is characterized when the upper boundfor the sectional curvatures of the ambient manifold is strictlynegative. Finally, when the sectional curvatures of N are boundedfrom above for any constant (positive or negative), it is provedthat the -isoperimetric quotient of the extrinsic balls is boundedfrom below by the mean curvature of the geodesic spheres inthe m-dimensional real space forms. 相似文献
20.
Ge DONG 《数学年刊B辑(英文版)》2021,42(3):333-356
In this paper, the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains. She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains. In both cases,coercive and noncoercive operators are handled. The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established. 相似文献