共查询到20条相似文献,搜索用时 15 毫秒
1.
Huai-Dong Cao Haizhong Li 《Calculus of Variations and Partial Differential Equations》2013,46(3-4):879-889
In this paper, we prove a classification theorem for self-shrinkers of the mean curvature flow with |A|2 ≤ 1 in arbitrary codimension. In particular, this implies a gap theorem for self-shrinkers in arbitrary codimension. 相似文献
2.
In this paper, we generalize Colding–Minicozzi’s recent results about codimension-1 self-shrinkers for the mean curvature flow to higher codimension. In particular, we prove that the sphere ${bf S}^{n}(\sqrt{2n})$ is the only complete embedded connected $F$ -stable self-shrinker in $\mathbf{R}^{n+k}$ with $\mathbf{H}\ne 0$ , polynomial volume growth, flat normal bundle and bounded geometry. We also discuss some properties of symplectic self-shrinkers, proving that any complete symplectic self-shrinker in $\mathbf{R}^4$ with polynomial volume growth and bounded second fundamental form is a plane. As a corollary, we show that there is no finite time Type I singularity for symplectic mean curvature flow, which has been proved by Chen–Li using different method. We also study Lagrangian self-shrinkers and prove that for Lagrangian mean curvature flow, the blow-up limit of the singularity may be not $F$ -stable. 相似文献
3.
Gregório Pacelli Bessa Leandro F. Pessoa Marco Rigoli 《Israel Journal of Mathematics》2018,226(2):703-736
In this paper we study non-compact self-shrinkers first in general codimension and then in codimension 1. We respectively prove some vanishing theorems giving rise to rigidity of the self-shrinker and then estimates involving the higher order mean curvatures for the oriented case. The paper ends with some results on their index when considered as appropriate \(\bar f\)-minimal hypersurfaces. 相似文献
4.
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
5.
We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect transversally a hyperplane through the origin. When such an intersection is compact, we deduce spectral information on the natural drifted Laplacian associated to the self-shrinker. These results go in the direction of verifying the validity of a conjecture by H.D. Cao concerning the polynomial volume growth of complete self-shrinkers. A finite strong maximum principle in case the self-shrinker is confined into a cylindrical product is also presented. 相似文献
6.
In this paper, we investigate the positive solutions of \(\mathfrak {L}u=0\) on a self-shrinker. First, we prove a global gradient estimate for the positive solutions, and obtain a strong Liouville theorem. Then by the generalized Laplacian comparison theorem for the distance function on a self-shrinker, we derive a local gradient estimate for the positive solutions. At last, we collect some applications of the local gradient estimate for the positive solutions on self-shrinkers. 相似文献
7.
We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rmm+n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove rigidity results under minor growth conditions in terms of the mean curvature or the image of Gauss maps. 相似文献
8.
Gradient Estimates and Harnack Inequalities for Positive Solutions of $$\mathfrak{L}u=\frac{\partial u}{\partial t}$$ L u = ∂ u ∂ t on Self-shrinkers
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In this paper, we investigate the positive solutions of Lu=∂u/∂t on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions. 相似文献
9.
In this paper, we study the Lagrangian F-stability and Hamiltonian F-stability of Lagrangian self-shrinkers. We prove a characterization theorem for the Hamiltonian F-stability of n-dimensional complete Lagrangian self-shrinkers without boundary, with polynomial volume growth and with the second fundamental form satisfying the condition that there exist constants \(C_0>0\) and \(\varepsilon <\frac{1}{16n}\) such that \(|A|^2\le C_0+\varepsilon |x|^2\). We characterize the Hamiltonian F-stability by the eigenvalues and eigenspaces of the drifted Laplacian. 相似文献
10.
It is our purpose to study complete self-shrinkers in Euclidean space. By making use of the generalized maximum principle for \(\mathcal {L}\)-operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in \(\mathbb R^3\). Ding and Xin (Trans Am Math Soc 366:5067–5085, 2014) have proved this result under the assumption of polynomial volume growth, which is removed in our theorem. 相似文献
11.
Our target in this paper is given upper bounds for the first stability eigenvalue of closed (compact without boundary) surfaces in a 3-Riemannian manifold endowed with a smooth density function. As consequence, we deduce a topological constraint for the existence of closed stable surfaces in non-negatively curved spaces and a result of no existence of closed stable self-shrinkers of the mean curvature flow in \(\mathbb {R}^{3}\). 相似文献
12.
Christodoulos E. Athanasiadis Sotiria Dimitroula Eleftheria Kikeri Konstantinos I. Skourogiannis 《Mathematical Methods in the Applied Sciences》2017,40(6):2071-2077
In this work, we study two operators that arise in electromagnetic scattering in chiral media. We first consider electromagnetic scattering by a chiral dielectric with a perfectly conducting core. We define a chiral Calderon‐type surface operator in order to solve the direct electromagnetic scattering problem. For this operator, we state coercivity and prove compactness properties. In order to prove existence and uniqueness of the problem, we define some other operators that are also related to the chiral Calderon‐type operator, and we state some of their properties that they and their linear combinations satisfy. Then we sketch how to use these operators in order to prove the existence of the solution of the direct scattering problem. Furthermore, we focus on the electromagnetic scattering problem by a perfect conductor in a chiral environment. For this problem, we study the chiral far‐field operator that is defined on a unit sphere and contains the far‐field data, and we state and prove some of its properties that are preliminaries properties for solving the inverse scattering problem. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
13.
Dragan DJURCIC Aleksandar TORGASEV 《数学学报(英文版)》2006,22(3):689-692
In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc. 相似文献
14.
15.
S. A. H. Cardona 《Annals of Global Analysis and Geometry》2013,44(4):455-469
We study the basic properties of Higgs sheaves over compact Kähler manifolds and establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we prove some properties of semistable Higgs sheaves. 相似文献
16.
Giorgio Laguzzi 《Archive for Mathematical Logic》2014,53(5-6):487-502
In this paper we analyse some notions of amoeba for tree forcings. In particular we introduce an amoeba-Silver and prove that it satisfies quasi pure decision but not pure decision. Further we define an amoeba-Sacks and prove that it satisfies the Laver property. We also show some application to regularity properties. We finally present a generalized version of amoeba and discuss some interesting associated questions. 相似文献
17.
研究了多目标优化问题的近似解. 首先证明了多面体集是 co-radiant集,并证明了一些性质. 随后研究了多面体集下多目标优化问题近似解的特殊性质. 相似文献
18.
研究了布尔矩阵的广义逆,首先引入了布尔矩阵的Drazin逆及Cline逆,利用布尔矩阵的性质证明了任意布尔矩阵均有Drazin逆,从而证得任意布尔矩阵均有Cline逆,且Cline唯一.而且,在A+存在的情况下Ac=A+.最后证明了Cline逆的一些性质. 相似文献
19.
In this paper, we introduce a new concept of hybrid multivalued mappings in Hilbert spaces. We then prove some properties and the existence of fixed points of these mappings. Further, we prove weak and strong convergence theorems for a finite family of hybrid multivalued mappings. 相似文献
20.
Daniel Andrén 《Discrete Applied Mathematics》2009,157(11):2515-2524
In this paper we discuss the two variable Ising polynomials in a graph theoretical setting. This polynomial has its origin in physics as the partition function of the Ising model with an external field. We prove some basic properties of the Ising polynomial and demonstrate that it encodes a large amount of combinatorial information about a graph. We also give examples which prove that certain properties, such as the chromatic number, are not determined by the Ising polynomial. Finally we prove that there exist large families of non-isomorphic planar triangulations with identical Ising polynomial. 相似文献