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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.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Volume preserving Gauss curvature flow of convex hypersurfaces in the hyperbolic space
双曲空间 凸超曲面 保体积 高斯曲率流
2023/5/15
In this talk, we discuss Y. Wei, B. Yang and T. Zhou’s preprint arXiv:2210.06035, in which they consider volume preserving curvature flows of smooth, closed and convex hypersurfaces in hyperbolic spac...
CURVATURE PINCHING ESTIMATE AND SINGULARITIES OF THE RICCI FLOW
SINGULARITIES CURVATURE PINCHING ESTIMAT
2015/8/17
In this paper, we first derive a pinching estimate on the traceless Ricci
curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then
we apply this estimate to study...
PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS
PRINCIPAL CURVATURE ESTIMATES THE CONVEX LEVEL SETS SEMILINEAR ELLIPTIC EQUATIONS
2014/4/3
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...
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 ...
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...
Warped product Einstein metrics over spaces with constant scalar curvature
Warped product Einstein metrics spaces constant scalar curvature
2011/2/21
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a pro...
There are few known examples of manifolds with positive sectional curvature in Riemannian
geometry. Until recently, they were all homogeneous spaces [Be, Wa, AW] and biquotients [E1,
E2, Ba], i.e., ...
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...
Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets
Fractal curvature measures Minkowski one-dimensional self-conformal sets
2011/2/28
We investigate intrinsic geometric properties of invariant sets of one-dimensional conformal iterated function systems. We show that for such a set F the fractal cur-vature measures exist, if and only...
Flippable tilings of constant curvature surfaces
Flippable tilings constant curvature surfaces
2011/1/19
We call “flippable tilings” of a constant curvature surface a tiling by “black” and “white” faces, so that each edge is adjacent to two black and two white faces (one of each on each side), the black ...
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...
On a General Linear Nonlocal Curvature Flow of Convex Plane Curves
General Linear Nonlocal Curvature Flow Convex Plane Curves
2011/1/17
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal cur-vature flow for convex closed plane curves and discuss the short time existence and asymptotic
convergence behavio...