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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：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...
CROSS CURVATURE FLOW ON LOCALLY HOMOGENOUS THREE-MANIFOLDS (I)
HOMOGENOUS THREE-MANIFOLDS CURVATURE FLOW
2015/8/17
Chow and Hamilton introduced the cross curvature flow on closed 3-
manifolds with negative or positive sectional curvature. In this paper, we study
the negative cross curvature flow in t...
Singularities of generic mean curvature flow.
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 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...
Uniqueness of compact tangent flows in Mean Curvature Flow
compact tangent flows Mean Curvature Flow Differential Geometry
2011/9/19
Abstract: We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given spacetime point consists of a closed, multiplicity-one, smoothly embedded self-similar shrin...
Long time existence of the symplectic mean curvature flow
symplectic mean curvature flow Long time Differential Geometry
2011/8/25
Abstract: Let $(M,\bar{g})$ be a K\"ahler surface with a constant holomorphic sectional curvature $k>0$, and $\Sigma$ an immersed symplectic surface in $M$. Suppose $\Sigma$ evolves along the mean cur...
The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature
Cross curvature flow geometric evolution equation negative sectional curvature monotonicity formula hyperbolic metric
2010/2/26
We consider the cross curvature flow, an evolution equation of metrics on 3-manifolds. We establish short time existence when the sectional curvature has a sign. In the case of negative sectional curv...