共查询到20条相似文献,搜索用时 15 毫秒
1.
Hai-Ping Fu 《Proceedings Mathematical Sciences》2010,120(4):457-464
Let M
n
(n ≥ 3) be an n-dimensional complete immersed $
\frac{{n - 2}}
{n}
$
\frac{{n - 2}}
{n}
-super-stable minimal submanifold in an (n + p)-dimensional Euclidean space ℝ
n+p
with flat normal bundle. We prove that if the second fundamental form of M satisfies some decay conditions, then M is an affine plane or a catenoid in some Euclidean subspace. 相似文献
2.
3.
Keomkyo Seo 《Archiv der Mathematik》2010,94(2):173-181
We prove that if an n-dimensional complete minimal submanifold M in hyperbolic space has sufficiently small total scalar curvature then M has only one end. We also prove that for such M there exist no nontrivial L
2 harmonic 1-forms on M. 相似文献
4.
5.
Rigidity of compact minimal submanifolds in a unit sphere 总被引:3,自引:0,他引:3
LetM be ann-dimensional compact minimal submanifold of a unit sphereS
n+p
(p2); and letS be a square of the length of the second fundamental form. IfS2/3n everywhere onM, thenM must be totally geodesic or a Veronese surface. 相似文献
6.
Claudio Gorodski 《Proceedings of the American Mathematical Society》2004,132(8):2441-2447
We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.
7.
Let M~n(n ≥ 4) be an oriented closed submanifold with parallel mean curvature in an(n + p)-dimensional locally symmetric Riemannian manifold N~(n+p). We prove that if the sectional curvature of N is positively pinched in [δ, 1], and the Ricci curvature of M satisfies a pinching condition, then M is either a totally umbilical submanifold, or δ = 1, and N is of constant curvature. This result generalizes the geometric rigidity theorem due to Xu and Gu[15]. 相似文献
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9.
K. Rajala 《Geometric And Functional Analysis》2005,15(5):1100-1127
We give a quantitative proof for a theorem of Martio, Rickman and V?is?l? [MRV] on the rigidity of the local homeomorphism
property of spatial quasiregular mappings with distortion close to one. The proof is based on a distortion theory established
by using two main tools. First, we use a conformal invariant between sphere families and components of their preimages under
quasiregular mappings. Secondly, we use Hall’s quantitative isoperimetric inequality result [H] to relate two different types
of distortion.
Received: April 2004 Revision: October 2004 Accepted: December 2004 相似文献
10.
O. Yu. Dashkova 《Journal of Mathematical Sciences》2010,169(5):636-643
We consider an R
G-module A over a commutative Noetherian ring R. Let G be a group having infinite section p-rank (or infinite 0-rank) such that C
G
(A) = 1, A/C
A
(G) is not a Noetherian R-module, but the quotient A/C
A
(H) is a Noetherian R-module for every proper subgroup H of infinite section p-rank (or infinite 0-rank, respectively). In this paper, it is proved that if G is a locally soluble group, then G is soluble. Some properties of soluble groups of this type are also obtained. 相似文献
11.
Kazuyuki Hasegawa 《Journal of Geometry》2005,83(1-2):57-64
We study harmonic sections of the normal bundles for submanifolds. Especially, the stability of certain harmonic sections
of the normal bundles for compact submanifolds in the spheres are considered. 相似文献
12.
Hermann König Vitali Milman 《Proceedings of the Steklov Institute of Mathematics》2013,280(1):191-207
We study rigidity and stability properties of the Leibniz and chain rule operator equations. We describe which non-degenerate operators V, T 1, T 2,A: C k (?) → C(?) satisfy equations of the generalized Leibniz and chain rule type for f, g ∈ C k (?), namely, V (f · g) = (T 1 f) · g + f · (T 2 g) for k = 1, V (f · g) = (T 1 f) · g + f · (T 2 g) + (Af) · (Ag) for k = 2, and V (f ○ g) = (T 1 f) ○ g · (T 2 g) for k = 1. Moreover, for multiplicative maps A, we consider a more general version of the first equation, V (f · g) = (T 1 f) · (Ag) + (Af) · (T 2 g) for k = 1. In all these cases, we completely determine all solutions. It turns out that, in any of the equations, the operators V, T 1 and T 2 must be essentially equal. We also consider perturbations of the chain and the Leibniz rule, T (f ○ g) = Tf ○ g · Tg + B(f ○ g, g) and T (f · g) = Tf · g + f · Tg + B(f, g), and show under suitable conditions on B in the first case that B = 0 and in the second case that the solution is a perturbation of the solution of the standard Leibniz rule equation. 相似文献
13.
14.
JIN Quanqin 《中国科学A辑(英文版)》2000,43(12):1279-1293
In this paper, we determine a large class of totally geodesic submanifolds of a compact Riemannian symmetric space. The stability
of these submanifolds in their ambient space is also determined. 相似文献
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16.
A. Ducrot 《Mathematical Methods in the Applied Sciences》2007,30(3):291-304
This paper is devoted to the study of multi‐dimensional travelling wave solution for a thermo‐diffusive model, describing the propagation of curved flames in an infinite cylinder. The linear dependence of the components of the reaction rate together with the existence of an ignition temperature ensure that the corresponding linearized operator does not satisfy the Fredholm property. A direct consequence is that solvability conditions for the linearized operator are not known and classical methods of nonlinear analysis cannot be directly applied. We prove in this paper existence results of such travelling waves, by first introducing a suitable re‐formulation of the equations and then by choosing suitable weighted spaces that allows us to move the essential spectrum away from zero. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
17.
A real one-dimensional analogue of Zdunik's dichotomy is proved,giving dynamical conditions for a multimodal map to have a measureof maximal entropy of dimension one. 相似文献
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