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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.
Convergence of approximate deconvolution models to the mean Magnetohydrodynamics Equations: Analysis of two models
Magnetohydrodynamics Large Eddy Simulation Deconvolution models
2012/6/27
We consider two Large Eddy Simulation (LES) models for the approximation of large scales of the equations of Magnetohydrodynamics (MHD in the sequel). We study two $\alpha$-models, which are obtained ...
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 ...
Range description for a spherical mean transform on the hyperbolic spaces
Range description the hyperbolic spaces Differential Geometry Analysis of PDEs
2011/8/31
Abstract: We consider the spherical mean transform $\mR(f)$ of a function $f$ defined on the hyperbolic space $\Hs^n$. Let $\uS \subset \Hs^n$ be the unit sphere centered at the origin, and $\mR_{\uS}...
Travelling graphs for the forced mean curvature motion in an arbitrary space dimension
forced mean curvature movement eikonal equation Hamilton-Jacobi equations viscosity solution
2011/8/25
Abstract: We construct travelling wave graphs of the form $z=-ct+\phi(x)$, $\phi: x \in \mathbb{R}^{N-1} \mapsto \phi(x)\in \mathbb{R}$, $N \geq 2$, solutions to the $N$-dimensional forced mean curvat...
The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
Hypersurfaces with constant mean curvature Rigidity Scalar curvature Clifford torus
2011/1/20
We generalize the second pinching theorem for minimal hypersurfaces in a sphere due to Peng-Terng, Wei-Xu, Zhang, and Ding-Xin to the case of hypersurfaces with small constant mean curvature. Let Mn b...
Uniqueness of the Foliation of Constant Mean Curvature Spheres in Asymptotically Flat 3-Manifolds
Uniqueness Foliation of Constant Mean Curvature Spheres Asymptotically Flat 3-Manifolds
2011/2/21
In this paper I study the constant mean curvature surface in asymp-totically flat 3-manifolds with general asymptotics. Under some weak condition, I prove that outside some compact set in the asymptot...
Compact Mean Convex Hypersurfaces and the Fundamental Group of Manifolds with Nonnegative Ricci Curvature
Compact Mean Convex Hypersurfaces Fundamental Group of Manifolds Nonnegative Ricci Curvature
2011/1/19
We show that the existence of an embedded compact, boundaryless hypersurface S of strictly
positive mean curvature in a noncompact, connected, complete Riemannian n-manifold N of non-
negative Ricci...
On the singular set of mean curvature flows with Neumann free boundary conditions
singular set of mean curvature flows Neumann free boundary conditions
2011/1/17
We consider n-dimensional hypersurfaces flowing by mean curvature flow with Neumann free
boundary conditions supported on a smooth support surface. We show that the Hausdorff n-measure of the singula...
A mean curvature estimate for cylindrically bounded submanifolds
mean curvature estimate cylindrically bounded submanifolds
2010/12/10
We extend the estimate obtained in [1] for the mean curvature of a cylindrically bounded proper submanifold in a product manifold with an Euclidean space as one factor to a general product ambient spa...
Darboux transforms and simple factor dressing of constant mean curvature surfaces
Darboux transforms simple factor dressing constant mean curvature surfaces
2010/12/14
We define a transformation on harmonic maps N : M ! S2 from a Riemann surface M into the 2–sphere which depends on a parameter μ 2 C, the so–called μ–Darboux transformation.
Ginzburg-Landau Vortex and Mean Curvature Flow with External Force Field
system of parabolic equations Ginzburg--Landau vortex mean curvature flow
2007/12/11
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-dimens...