共查询到20条相似文献,搜索用时 0 毫秒
1.
This paper mainly deals with the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a Kähler surface. The relation between the maximum of the Kähler angle and the maximum of |H|2 on the limit flow is studied. The authors also show the nonexistence of type II blow-up flow of a symplectic mean curvature flow which is normal flat or of an almost calibrated Lagrangian mean curvature flow which is flat. 相似文献
2.
The authors mainly study the generalized symplectic mean curvature flow in an almost Einstein surface, and prove that this flow has no type-I singularity. In the graph case, the global existence and convergence of the flow at infinity to a minimal surface with metric of the ambient space conformal to the original one are also proved. 相似文献
3.
In this paper, we study the singularities of the mean curvature ?ow from a symplectic surface or from a Lagrangian surface in a K?hler-Einstein surface. We prove that the blow-up ?ow ∑ s ∞ at a singular point(X 0, T 0) of a symplectic mean curvature ?ow Σt or of a Lagrangian mean curvature ?ow Σt is a nontrivial minimal surface in ? 4 , if ∑ - ∞ ∞ is connected. 相似文献
4.
Henri Anciaux 《Geometriae Dedicata》2006,120(1):37-48
We give new examples of self-shrinking and self-expanding Lagrangian solutions to the Mean Curvature Flow (MCF). These are Lagrangian submanifolds in
, which are foliated by (n − 1)-spheres (or more generally by minimal (n − 1)-Legendrian submanifolds of
), and for which the study of the self-similar equation reduces to solving a non-linear Ordinary Differential Equation (ODE). In the self-shrinking case, we get a family of submanifolds generalising in some sense the self-shrinking curves found by Abresch and Langer. 相似文献
5.
Knut Smoczyk 《Mathematische Nachrichten》2001,229(1):175-186
We derive a one to one correspondence between conformal solitons of the mean curvature flow in an ambient space N and minimal submanifolds in a different ambient space where equals ℝ × N equipped with a warped product metric and show that a submanifold inN converges to a conformal soliton under the mean curvature flow in N if and only if its associatedsubmanifold in converges to a minimal submanifold under a rescaled mean curvature flow in . We then define a notion of stability for conformal solitons and obtain Lp estimates as well as pointwise estimates for the curvature of stable solitons. 相似文献
6.
K. Smoczyk 《Geometriae Dedicata》2002,91(1):59-69
We formulate and apply a modified Lagrangian mean curvature flow to prescribe the Maslov form of Lagrangian immersions in
n
. We prove longtime existence results and derive optimal results for curves. 相似文献
7.
The main result of this paper states that the traceless second fundamental tensor A0 of an n-dimensional complete hypersurface M, with constant mean curvature H and finite total curvature, M |A0|n dvM < , in a simply-connected space form
(c), with non-positive curvature c, goes to zero uniformly at infinity. Several corollaries of this result are considered: any such hypersurface has finite index and, in dimension 2, if H
2 + c > 0, any such surface must be compact. 相似文献
8.
9.
10.
本文估计了空间形式Nn+1(c)中常平均曲率超曲面上共形度量的曲率上界,并用其研究了Nn+1(c)中常平均曲率超曲面的强稳定性. 相似文献
11.
Rafael Lopez 《Geometriae Dedicata》1997,66(3):255-263
This paper proves that an embedded compact surface in the Euclidean space with constant mean curvature H bounded by a circle of radius 1 and included in a slab of width
is a spherical cap. Also, we give partial answers to the problem when a surface with constant mean curvature and planar boundary lies in one of the halfspaces determined by the plane containing the boundary, exactly, when the surface is included in a slab. 相似文献
12.
Qi DING 《数学年刊B辑(英文版)》2011,32(1):27-44
In this paper, the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally
symmetric spaces is studied. It is proved that the flow converges to a unique geodesic sphere, i.e., every principle curvature
of the hypersurfaces converges to a same constant under the flow. 相似文献
13.
14.
We give a complete classification of complete noncompact oriented surfaces with nonnegative Gaussian curvature and finite total mean curvature in R3. 相似文献
15.
本文利用[5]的方法,对R4(C)中平均曲率方向平行的Bonnet曲面引入了半测地等温 参数,并给出了一个分类结果. 相似文献
16.
Ildefonso Castro Francisco Urbano 《Proceedings of the American Mathematical Society》2004,132(6):1797-1804
We characterize the Lagrangian pseudosphere as the only branched Lagrangian immersion of a sphere in complex Euclidean plane with constant length mean curvature vector.
17.
Huai Yu JIAN Yan Nan LIU 《数学学报(英文版)》2006,22(6):1831-1842
This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow. 相似文献
18.
The Blow-up Locus of Heat Flows for Harmonic Maps 总被引:5,自引:0,他引:5
Abstract
Let M and N be two compact Riemannian manifolds. Let u
k
(x, t) be a sequence of strong stationary weak heat flows from M×R
+ to N with bounded energies. Assume that u
k→u weakly in H
1, 2(M×R
+, N) and that Σt is the blow-up set for a fixed t > 0. In this paper we first prove Σt is an H
m−2-rectifiable set for almost all t∈R
+. And then we prove two blow-up formulas for the blow-up set and the limiting map. From the formulas, we can see that if the
limiting map u is also a strong stationary weak heat flow, Σt is a distance solution of the (m− 2)-dimensional mean curvature flow [1]. If a smooth heat flow blows-up at a finite time, we derive a tangent map or a weakly
quasi-harmonic sphere and a blow-up set ∪t<0Σt× {t}. We prove the blow-up map is stationary if and only if the blow-up locus is a Brakke motion.
This work is supported by NSF grant 相似文献
19.
In this paper we show how to embed a time slice of the Schwarzchild spacetime that models the outer space around a massive star, as a Lagrangian submanifold invariant under the standard action of the special orthogonal group on complex Euclidean space. This result is generalized for rotationally invariant metrics that can be considered as higher-dimensional versions of Schwarzchild's and these submanifolds are locally characterized as the only ones with zero scalar curvature inside the above family. 相似文献
20.
Consider a hypermanifold M
0 of a Riemannian manifold N whose Riccicurvature is bounded from below. If M
0 is transversal to a conformalvector field on N, then conditions are given, such that the meancurvature evolution of M
0 with Dirichlet boundary conditions has asolution for all times. 相似文献