关于《2型球面超曲面》一文的注记

本文证明了2型球面紧致超曲面是1型的，因而是质量对称的．换言之，不存在2型球面紧致超曲面，推广了文［2，3，4，5」中的结论．     

紧致超曲面上的谱

设Ｍ是Ｓ^n 1(1)上的紧致极小超曲面,Ｍ１,n-1是Ｓ^(n 1)(1)上的Ｃlifford极小超曲面。若它们的谱相同,则它们是墙虎的。对于Ｓ^(n 1)(1)上的紧致常平均曲率超曲面和Ｈ（r)－环,在某些条件下等谱可推出等距。     

2型球面超曲面

本文证明了2型球面紧致超曲面具有常纯量曲率和常平均曲率，因而是质量对称的．     

双曲空间形式中具有常平均曲率的超曲面(英文)

本文研究了双曲空间形式H~(n+1)(—1)中具有常平均曲率及两个离散主曲率(其中一个主曲率是1-重)的完备连通可定向的n-维超曲面M~n.利用活动标架,得到如果M~n的基本形式的模长满足刚性条件(1.3),那么M~n同构双曲柱面.     

局部对称流形中具常平均曲率的完备超曲面

本文研究了局部对称流形中具常平均曲率的完备超曲面，得到了这种超曲面的一个特征定理，推广了H．Alencar和M．do Carmo以及N．X．Shui和G．Q．Wu的结果。     

H~3(c)中常平均曲率曲面的稳定性

设M是3维双曲空间H~3(c)中常平均曲率曲面,本文通过估计M上共形度量的Gauss曲率,研究了其稳定性.     

De Sitter空间的2-调和超曲面

设M是de sitter空间S1^n 1(1)的紧致2－调和类空超曲面，获得了关于M的第二基本形式模长平方的Pinching结果。     

某些特殊曲面和子流形的等周不等式

本文讨论了Ｒ３内具常平均曲率曲面的等周不等式对于欧氏空间内极小子流形，假如子流形的边界具备某些特殊条件，给出了一个结果     

THE GAUSS MAP OF TIMELIKE SURFACES IN R_1~n

ＴＨＥＧＡＵＳＳＭＡＰＯＦＴＩＭＥＬＩＫＥＳＵＲＦＡＣＥＳＩＮＲ_１~ｎ￥ＨＯＮＧＪＩＡＮＱＩＡＯＡｂｓｔｒａｃｔ：Ｇａｕｓｓｍａｐｓｏｆｏｒｉｅｎｔｅｄｔｉｍｅｌｉｋｅ２－ｓｕｒｆａｃｅｓｉｎａｒｅｃｈａｒａｃｔｅｒｉｚｅｄ,ａｎｄｉｔｉｓｓｈｏｗｎ...     

n维双曲空间中给定Gauss映照的曲面的Weierstrass表示

将双曲上半空间Hn中的曲面视为Rn中的曲面,导出这两种共形浸入下平均曲率向量的关系;证明了这两种浸入下Gauss映照是一样的;给出Hn中给定Gauss映照的曲面的Weierstrass表示;证明了一个唯一性结果.     

LIMITATIONS ON PRESCRIBING THE HOPF DIFFERENTIAL FOR MINIMAL SURFACES IN H3

ABSTRACT

The Hopf map from minimal surfaces in H ³ to holomorphic quadratic differentials on H ² is considered. Whether or not a given quadratic differential is in the image of this map is determined by the global existence/non-existence of solutions to a certain quasi-linear PDE. It is shown that this map is not surjective.     

SUBGROUPS OF THE FREE SEMIGROUP ON A BIORDERED SET IN WHICH PRINCIPAL IDEALS ARE SINGLETONS

ABSTRACT

Easdown has conjectured that the subgroups of the free semigroup on an arbitrary biordered set are free. In this note a weaker conjecture is verified. It is shown that the subgroups of the free semigroup on a biordered set in which principal ideals are singletons are free. In addition, an expression is given for the ranks of the maximal subgroups. This generalizes a result due to Pastijn which involves the free semigroup on a rectangular biset.     

关于"Banach空间中非线性脉冲Volterra型积分方程的可解性"一文的商榷

举出反例指出《Banach空间中非线性脉冲Volterra型积分方程的可解性》(洪世煌,系统科学与数学. 2004, 22(2))一文主要结论的不妥之处,并提出文中在定理证明中的问题.     

ON THE TOPOLOGY,VOLUME,DIAMETER AND GAUSS MAP IMAGE OF SUBMANIFOLDS IN A SPHERE

In this paper, the author uses Gauss map to study the topology, volume and diameter of submanifolds in a sphere. It is proved that if there exist ε, 1≥ε > 0 and a fixed unit simple p-vector a such that the Gauss map g of an n-dimensional complete and connected submanifold M in Sn p satisfies (g, a) ≥ε, then M is diffeomorphic to Sn, and the volume and diameter of M satisfy εnvol(Sn) ≤vol(M) ≤ vol(Sn)/ε and επ ≤diam(M) ≤ π/ε, respectively. The author also characterizes the case where these inequalities become equalities. As an application, a differential sphere theorem for compact submanifolds in a sphere is obtained.     

范畴中态射集星型序的若干研究

本文证得星型序的乘法性质、遗传性质及其在偏序下态射广义逆的从属性质，并将星序的Hartwig上确界定理推广到带有对合*的正性预加法范畴中．