单位球面的超曲面的一个内蕴刚性定理

设M是单位球面S^n 1无脐点超曲面,在S^n 1 Moebius变换群下M的基本不变量是Moebius度量g,Moebius形式Φ,Moebius第二基本形式B和Biaschke张量A。本文我们证明如下主要定理：设x：M→S^n 1是S^n 1的无脐点超曲面,n≥3,Q和K分别是M关于Moebius度量的Ricci曲率的下确界和正规数量曲率,如果Moebius形式Φ平行,Q-K≥(n-2/n)^2,那么n为偶数且x：M→S^n 1 Moebius等价于Clifford极小环x:S^n/2(1/2)→S^n 1。     

Commuting finite Blaschke products with no fixed points in the unit disk

In this paper we study when two finite Blaschke products commute. We complete previous results by Chalendar and Mortini (when they have a fixed point in the unit disk) and by Arteaga (when they do not have a fixed point in the unit disk).     

SUBMANIFOLDS IN S~(n+p) WITH PARALLEL MBIUS FORM

§ 1　IntroductionLet x:M→ Sn+p be an n-dimensional submanifold in the unit sphere without umbilicpoints.Let { ei} be a local orthonormal basis with respectto the firstfundamental form I=dx·dx with dual basis{ θi} .Let II =∑ijαhαijθiθjeαbe the second fundamental form of xand H =∑αHαeαbe the mean curvature vector of x,where we use the range of indices:1≤ i,j,k,l≤ n,　　 n + 1≤α,β,γ≤ n + p,Hα=1n∑ihαij,{ eα} is a local orthonormal basis forthe normal bundle ofx.We defi…     

关于Hilbert不等式及其应用

设a,b为任意复数,证明了如下的不等式:其中A=A(a,b)为一实数。此不等式显然为Hilber不等式有意义的改进。 若b=a,则上述不等式中可取。应用此结果,立即得到Fejer-Riesz型不等式。     

Projective Blaschke manifolds

In this paper we define the concept of projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. partially supported by NSFC 10771146 and RFDP(20060610004)