搜索结果: 1-15 共查到“数学 Mean curvature”相关记录43条 . 查询时间(0.052 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds
紧致流形 sigma-2曲率 边界平均曲率
2023/11/15
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mean curvature flow coming out of cones
圆锥体 流出 平均曲率流
2023/4/13
We study mean curvature flows (MCFs) coming out of cones. As cones are singular at the origin, the evolution is generally not unique. A special case of such flows is known as the self-expanders. We wi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent Developments in Constant Mean Curvature Hypersurfaces
恒定 平均曲率 超曲面
2023/4/13
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mean Curvature Flow Translators
平均曲率流 转换器 Ilmanen弱平均曲率流 椭圆正则化构造
2023/4/18
Mean curvature flow is the fastest way to decrease the area of surfaces. It is the model in many disciplines such as material science, fluid mechanism, and computer graphics. The translators are a spe...
Existence and regularity of extremal solutions for a mean-curvature equation
Mean curvature minimal solution semi-stable solution extremal solution regularity
2015/10/15
We study a class of mean curvature equations −Mu = H +λup where M denotes the mean curvature operator and for p ≥ 1. We show that there exists an extremal parameter λ∗ such that this equat...
Singularities of generic mean curvature flow.
MEAN CURVATURE FLOW OF HIGHER CODIMENSION IN RIEMANNIAN MANIFOLDS
MEAN CURVATURE HIGHER CODIMENSION RIEMANNIAN MANIFOLDS
2018/4/19
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
On complete constant mean curvature vertical multigraphs in E(κ,τ)
multigraphs constant mean curvature homogeneous spaces
2012/6/29
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a cons...
Motion by Volume Preserving Mean Curvature Flow Near Cylinders
Motion by Volume Mean Curvature Flow Cylinders Analysis of PDEs
2012/5/24
Center manifold analysis can be used in order to investigate the stability of the stationary solutions of various PDEs. This can be done by considering the PDE as an ODE between certain Banach spaces ...
Mean curvature flows and isotopy problems
Mean curvature flows isotopy problems Differential Geometry
2012/4/23
In this note, we discuss the mean curvature flow of graphs of maps between Riemannian manifolds. Special emphasis will be placed on estimates of the flow as a non-linear parabolic system of differenti...
Mean curvature flow of higher codimension in Riemannian manifolds
Mean curvature flow submanifolds convergence theorem curvature pinching Riemannian manifolds
2012/4/17
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching conditio...
Mean curvature flow of higher codimension in hyperbolic spaces
Mean curvature higher codimension hyperbolic spaces
2018/4/19
In this paper we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms. Particularly, we prove that the mean curvature flow deforms a...
The extension and convergence of mean curvature flow in higher codimension
extension convergence mean curvature higher codimension
2018/4/19
In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension d 1, which generalizes the extension t...
Mean curvature flow of Lagrangian submanifolds with isolated conical singularities
Lagrangian submanifolds isolated conical singularities Differential Geometry
2011/9/20
Abstract: In this paper we study the short time existence problem for the (generalized) Lagrangian mean curvature flow in (almost) Calabi--Yau manifolds when the initial Lagrangian submanifold has iso...
Change of Topology in Mean Convex Mean Curvature Flow
Change of Topology Mean Convex Mean Curvature Flow Differential Geometry
2011/9/19
Abstract: Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy g...