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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integral equations with bubble-type kernel via the method of moving spheres
运动球体 气泡型核 积分方程
2023/4/27
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...
Stretching Three-Holed Spheres and the Margulis Invariant
Margulis Invariant Three-Holed Spheres
2015/9/29
This paper applies the authors’ forthcoming work, ”Affine deformations of a three-holed sphere” in Lorentzian geometry to prove a result in
hyperbolic geometry. Namely, an infinitesimal de...
For any linear quotient of a sphere, X = Sn−1/Γ, where Γ is an elementary abelian p–group, there is a corresponding Fp representable matroid MX which only depends on the isometry class of X. Whe...
Maximization of the second conformal eigenvalue of spheres
Maximization the second conformal eigenvalue spheres Spectral Theory
2012/6/14
We establish in this paper an upper bound on the second eigenvalue of n-dimensional spheres in the conformal class of the round sphere. This upper bound holds in all dimensions and is asymptotically s...
The Complex of Non-separating embedded spheres
Complex of Non-separating embedded spheres Geometric Topology
2012/4/17
For n >2, we shall show that the group Aut(NS(M)) of simplicial automorphisms of the complex NS(M) of non-separating embedded spheres in the manifold M,connected sum of n copies of S^2 X S^1, isomorph...
Yang-Mills connections of cohomogeneity one on SO(n)-bundles over Euclidean spheres
Yang-Mills connections of cohomogeneity one SO(n)-bundles Euclidean spheres Differential Geometry
2011/9/23
Abstract: We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation ...
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
homogeneous solutions Yamabe problem spheres Differential Geometry
2011/9/21
Abstract: We study existence and non existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all ...
Classification of 3-bridge spheres of 3-bridge arborescent links
3-bridge spheres 3-bridge arborescent links Geometric Topology
2011/8/26
Abstract: In this paper, we give an isotopy classification of 3-bridge spheres of 3-bridge arborescent links, which are not Montesinos links. To this end, we prove a certain refinement of a theorem of...
Spheres with more than 7 vector fields: all the fault of Spin(9)
Spin(9) octonions vector fields on spheres
2011/8/24
Abstract: We give an interpretation in terms of the Lie group Spin(9) of the maximal number of linearly independent vector fields on odd dimensional spheres.
Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres
Confinement Nonperturbative Effects QCD
2011/3/2
We study the covariantly constant Savvidy-type chromomagnetic vacuum in finite-temperature
Yang-Mills theory on the four-dimensional curved spacetime. Motivated by the fact that a positive spatial cu...
On the existence of exotic homotopy 3-spheres
Homotopy spheres 3-manifold topology Morse theory
2011/1/17
This paper gives a geometric topological proof that exotic ho-motopy 3-spheres do not exist.
It is shown, non–rigorously, that the effective action on Z q– factored odd spheres (lunes) has a vanishing derivative at q = 1. This leaves the effective action on the ordinary sphere as (minus) the ...
On intersection of two embedded spheres in 3-space
intersection two embedded spheres 3-space
2011/1/18
We find necessary and sufficient conditions on sequences x = x1, x2, . . . , xn, y = y1, y2, ..., yn of positive integers, for existence of embeddings f, g : S2 → R3 such that S2 − g−1(S2)...
A Geometric Representation of Improper Indefinite Affine Spheres with Singularities
Improper affine spheres Area distances Affine symmetry sets
2011/1/20
We consider in this paper a class of improper indefinite affine spheres with singularities in R3 called indefinite improper affine maps.We propose a representation of surfaces in this class by a pair ...
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...