共查询到20条相似文献,搜索用时 20 毫秒
1.
Lu Wang 《Geometriae Dedicata》2011,151(1):297-303
In this paper, we prove that smooth self-shrinkers in mathbb Rn+1{mathbb R^{n+1}}, that are entire graphs, are hyperplanes. Previously, Ecker and Huisken showed that smooth self-shrinkers, that are entire graphs and have at most polynomial growth, are hyperplanes. The point of this paper is that no growth assumption at infinity is needed. 相似文献
2.
HAN Ying-bo 《高校应用数学学报(英文版)》2009,24(1)
In this paper, a Bernstein type theorem for minimal Lagrangian submanifolds in quaternion Euclidean space Hn is studied. 相似文献
3.
The stable mixed volume of the Newton polytopes of a polynomial system is defined and shown to equal (genetically) the number
of zeros in affine space Cn. This result refines earlier bounds by Rojas, Li, and Wang [5], [7], [8]. The homotopies in [4], [9], and [10] extend naturally
to a computation of all isolated zeros in Cn
This research was supported by the David and Lucile Packard Foundation and the National Science Foundation. 相似文献
4.
Ying-bo Han 《高校应用数学学报(英文版)》2009,24(1):114-118
In this paper, a Bernstein type theorem for minimal Lagrangian submanifolds in quaternion Euclidean space H^n is studied. 相似文献
5.
Lei Ni 《Proceedings of the American Mathematical Society》2002,130(4):1207-1210
We show that any minimal volume preserving map from the Euclidean plane into itself is a linear diffeomorphism. We derive this from a similar result on minimal diffeomorphisms. We also show that the classical Bernstein theorem on minimal graphs is a corollary of our result.
6.
We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface M in \({\mathbb{R}^{n+1}}\). (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that M has only essential spectrum consisting of the half line [0, +∞). This is the case when \({{\rm lim}_{\tilde{r}\to +\infty}\,\tilde{r}\kappa_i=0}\), where \({\tilde{r}}\) is the extrinsic distance to a point of M and κ i are the principal curvatures. (2) If the κ i satisfy the decay conditions \({|\kappa_i|\leq 1/\tilde{r}}\) and strict inequality is achieved at some point \({y\in M}\), then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces. 相似文献
7.
This note chronicles various roles played by the Yasuda-Shimada theorem in some recent developments of Riemann--Finsler geometry. We shall demonstrate that the said theorem is, at various stages of its life, an enigma, an inspiration, a flawed icon, and a powerful catalyst. 相似文献
8.
Bing Ye Wu 《Annals of Global Analysis and Geometry》2007,31(4):375-384
Let
be a Minkowski 3-space of Randers type with
, where
is the Euclidean metric and
. We consider minimal surfaces in
and prove that if a connected surface M in
is minimal with respect to both the Busemann–Hausdorff volume form and the Holmes–Thompson volume form, then up to a parallel
translation of
, M is either a piece of plane or a piece of helicoid which is generated by lines screwing about the x
3-axis.
相似文献
9.
Huai-Dong Cao Ying Shen Shunhui Zhu 《Calculus of Variations and Partial Differential Equations》1998,7(2):141-157
We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski
space into the hyperbolic space. As an application, we prove a Bernstein theorem which says that if the image of the Gauss
map is bounded from one side, then the spacelike constant mean curvature hypersurface must be linear. This result extends
the previous theorems obtained by B. Palmer [Pa] and Y.L. Xin [Xin1] where they assume that the image of the Gauss map is
bounded. We also prove a Bernstein theorem for spacelike complete surfaces with parallel mean curvature vector in four-dimensional
spaces.
Received July 4, 1997 / Accepted October 9, 1997 相似文献
10.
Baoqiang Wu 《Proceedings of the American Mathematical Society》2004,132(1):211-215
In this paper we prove a general Bernstein theorem on the complete spacelike constant mean curvature hypersurfaces in Minkowski space. The result generalizes the previous result of Cao-Shen-Zhu (1998) and Xin (1991). The proof again uses the fact that the Gauss map of a constant mean curvature hypersurface is harmonic, which was proved by K. T. Milnor (1983), and the maximum principle of S. T. Yau (1975).
11.
《Mathematische Nachrichten》2017,290(4):570-582
The contribution of this paper is two‐fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing vector field, by considering the Busemann–Hausdorff measure and Holmes–Thompson measure simultaneously. The second one is to obtain the explicit local expressions of two types of nontrivial rotational BH‐minimal surfaces in a Randers domain of constant flag curvature , which are the first examples of BH‐minimal surfaces in the hyperbolic Randers space. 相似文献
12.
A Bernstein theorem for special Lagrangian graphs 总被引:2,自引:0,他引:2
We obtain a Bernstein theorem for special Lagrangian graphs in for arbitrary n only assuming bounded slope but no quantitative restriction.
Received: 18 January 2001 / Accepted: 7 June 2001 / Published online: 12 October 2001
The second-named author is grateful to the Max Planck Institute for Mathematics in the Sciences in Leipzig for its hospitality
and support and also 973 project in China. 相似文献
13.
We obtain, in any dimension N and for a large range of values of θ, a Bernstein theorem for the fourth-order partial differential equation of affine maximal type assuming the completeness of Calabi's metric. This contains the results of Li–Jia [A.M. Li, F. Jia, Ann. Glob. Anal. Geom. 23 (2003)] for affine maximal equations and of Zhou [B. Zhou, Calc. Var. Partial Differ. Equ. 43 (2012)] for Abreu's equation. In particular, we extend the result of Zhou from to . 相似文献
14.
15.
A NOTE ON BERNSTEIN TYPE OPERATORS 总被引:2,自引:0,他引:2
In this note we give a counterexample to a result of Z.Ditzian and K.Ivanov.A directtheorm on C[0,1]is also presented for Kantorovich operators and Bernstein-Durrmeyer op-erators. 相似文献
16.
A celebrated theorem of Coburn asserts that, on the setting of the Hardy space, if a Toeplitz operator is nonzero, then either it is one-to-one or its adjoint operator is one-to-one. In this paper, we show that an analogous result holds for Toeplitz operators acting on the Dirichlet space. 相似文献
17.
18.
We prove the following Hartogs-Bochner type theorem: Let M be a connected C2 hypersurface of Pn(C) (n≥2) which divides Pn(C) in two connected open sets Ω1 and Ω2. Suppose that M has at most one open CR orbit. Then there exists i∈{1,2} such that C1 CR functions defined on M extends holomorphically to Ω
i
.
Supported by the TMR network. 相似文献
19.