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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...
FIRST VARIATION OF THE GENERAL CURVATURE-DEPENDENT SURFACE ENERGY
Surface energy gradient fl ow mean curvature
2015/12/11
We consider general surface energies, which are weighted integrals
over a closed surface with a weight function depending on the position, the
unit normal and the total curvature of the surface. Ene...
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...
Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
Singularities of generic mean curvature flow.
An obstructions to Non-negative curvature on Bundles with Pull-back connections
nonegative sectional curvature riemannian submersions exotic spheres
2012/6/30
Motivated to study the geometry of the exotic spheres constructed in [5], we derive a necessary condition for non-negative sectional curvature in certain total spaces of Riemannian submersions with to...
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...
Nullspaces of Conformally Invariant Operators. Applications to $Q_{k}$-curvature
Spectral geometry conformal geometry nodal sets Qk-curvature
2012/6/19
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfu...
Collapsing 4-manifolds under a lower curvature bound
collapsing Gromov-Hausdorff convergence Alexandrov spaces topology of 4-manifolds
2012/5/24
In this paper we describe the topology of 4-dimensional closed orientable Riemannian manifolds with a uniform lower bound of sectional curvature and with a uniform upper bound of diameter which collap...
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...
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Ricci curvature metric measure spaces branching metric spaces Differential Geometry
2012/3/1
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy ...
Curvature properties of pseudo-sphere bundles over paraquaternionic manifolds
twistor space Einstein manifold paraquaternionic structure mixed 3-structure
2011/9/21
Abstract: In this paper we obtain several curvature properties of the twistor and reflector spaces of a paraquaternionic K\"{a}hler manifold and prove the existence of both positive and negative mixed...
On the curvature of G-manifolds with finitely many non-principal orbits
G-manifold cohomogeneity Ricci curvature
2011/9/20
Abstract: We investigate the curvature of invariant metrics on G-manifolds with finitely many non-principal orbits. We prove existence results for metrics of positive Ricci curvature and non-negative ...