共查询到20条相似文献,搜索用时 0 毫秒
1.
F.E.C. Camargo R.M.B. Chaves L.A.M. Sousa Jr. 《Differential Geometry and its Applications》2008,26(6):592-599
In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space , n?3, with constant normalized scalar curvature R satisfying totally umbilical? 相似文献
2.
Maria Fernanda Elbert Barbara Nelli Harold Rosenberg 《Proceedings of the American Mathematical Society》2007,135(10):3359-3366
Let be a Riemannian manifold with sectional curvatures uniformly bounded from below. When we prove that there are no complete (strongly) stable -hypersurfaces, without boundary, provided is large enough. In particular, we prove that there are no complete strongly stable -hypersurfaces in without boundary,
3.
4.
Stability of hypersurfaces with constant mean curvature 总被引:12,自引:0,他引:12
5.
Let M^n be an n-dimensional complete noncompact oriented weakly stable constant mean curvature hypersurface in an (n + 1)-dimensional Riemannian manifold N^n+1 whose (n - 1)th Ricci curvature satisfying Ric^N(n-1) (n - 1)c. Denote by H and φ the mean curvature and the trace-free second fundamental form of M respectively. If |φ|^2 - (n- 2)√n(n- 1)|H||φ|+ n(2n - 1)(H^2+ c) 〉 0, then M does not admit nonconstant bounded harmonic functions with finite Dirichlet integral. In particular, if N has bounded geometry and c + H^2 〉 0, then M must have only one end. 相似文献
6.
7.
Jui-Tang Ray Chen 《Annals of Global Analysis and Geometry》2009,36(2):161-190
This article concerns the structure of complete noncompact stable hypersurfaces M
n
with constant mean curvature H > 0 in a complete noncompact oriented Riemannian manifold N
n+1. In particular, we show that a complete noncompact stable constant mean curvature hypersurface M
n
, n = 5, 6, in the Euclidean space must have only one end. Any such hypersurface in the hyperbolic space with
, respectively, has only one end. 相似文献
8.
In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature
(cmc) 1 in (Delaunay unduloids). When n=3, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite
topology cmc 1 surfaces with properly embedded ends. Similar results are obtained for hypersurfaces with cmc bigger than 1
in hyperbolic space.
Received: 6 July 2000; in final form: 10 September 2000 / Published online: 25 June 2001 相似文献
9.
Xu Cheng 《Archiv der Mathematik》2006,86(4):365-374
We discuss the non-existence of complete noncompact constant mean curvature hypersurfaces with finite index in a 4- or 5-dimensional
manifold. As a consequence, we obtain that a complete noncompact constant mean curvature hypersurface in
with finite index must be minimal.
Received: 30 May 2005 相似文献
10.
The partitioning problem for a smooth convex bodyB 3 consists in to study, among surfaces which divideB in two pieces of prescribed volume, those which are critical points of the area functional.We study stable solutions of the above problem: we obtain several topological and geometrical restrictions for this kind of surfaces. In the case thatB is a Euclidean ball we obtain stronger results.Antonio Ros is partially supported by DGICYT grant PB91-0731 and Enaldo Vergasta is partially supported by CNPq grant 202326/91-8. 相似文献
11.
Fang Jia 《Differential Geometry and its Applications》2005,22(2):199-214
Let be a locally strongly convex hypersurface, given by a strictly convex function xn+1=f(x1,…,xn) defined in a convex domain Ω⊂An. We consider the Riemannian metric G# on M, defined by . In this paper we prove that if M is a locally strongly convex surface with constant affine mean curvature and if M is complete with respect to the metric G#, then M must be an elliptic paraboloid. 相似文献
12.
In this paper, we completely classify complete hypersurfaces inR
4 with constant mean curvature and constant scalar curvature.The project was supported by NNSFC, FECC, and CPF. 相似文献
13.
Leung-Fu Cheung 《manuscripta mathematica》1991,70(1):219-226
Summary In this paper we present sufficient conditions for the non-existence of stable, complete, noncompact, constant mean curvature
hypersurfaces in certain (n+1)-dimensional Riemannian manifolds. 相似文献
14.
Rolf Walter 《Mathematische Annalen》1985,270(1):125-145
15.
In this work we consider a complete submanifold M with parallel mean curvature vector h immersed in a space form of constant sectional curvature c £ 0c\leq 0. If M has finite total curvature and |H|2 > -c|H|^2>-c, we prove that M must be compact. 相似文献
16.
17.
Fei-Tsen Liang 《Annali dell'Universita di Ferrara》2002,48(1):189-217
We consider the problem of determining the existence of absolute apriori gradient bounds of nonparametric hypersurfaces of
constant mean curvature in ann-dimensional sphereB
R, 1>R>R
0
(n)
, (R
0
(n)
being a constant depending only onn), without imposing boundary conditions or bounds of any sort.
Sunto Consideriamo il problema di determinare stime a priori di gradienti di ipersuperfici non parametriche di curvatura media costante in una sferan-dimensionaleB R, 1>R>R 0 (n), (R 0 (n) essendo una costante che dipende solo dan), senza imporre condizioni al contorno o limiti di altro tipo.相似文献
18.
局部对称流形中具有常平均曲率的完备超曲面 总被引:1,自引:0,他引:1
讨论了局部对称黎曼流形中具有常平均曲率的完备超曲面的性质,通过Laplace算子的计算,得到一个关于第二基本形式模长平方S的拼挤定理,推广了已有的结果. 相似文献
19.
In this paper, a complete space-like hypersurface with constant normal scalar curvature in a locally symmetric Lorentz space is discussed. The rigidity theorem is proved by using the operator □ introduced by S. Y. Cheng and S. T. Yau, and the result is a partially affirmative answer to the question posed by Haizhong Li in 1997. 相似文献
20.
It is known that the totally umbilical hypersurfaces in the (n + 1)-dimensional spheres are characterized as the only hypersurfaces with weak stability index 0. That is, a compact hypersurface with constant mean curvature, cmc, in S n+1, different from an Euclidean sphere, must have stability index greater than or equal to 1. In this paper we prove that the weak stability index of any non-totally umbilical compact hypersurface ${M \subset S^{{n+1}}}$ with cmc cannot take the values 1, 2, 3 . . . , n. 相似文献