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赵培标 《应用数学》1998,11(2):128-130
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.  相似文献   

3.
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。  相似文献   

4.
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.  相似文献   

5.
韩英波  冯书香 《数学杂志》2014,34(4):633-639
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.  相似文献   

6.
李海中 《数学学报》1991,34(5):599-603
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.  相似文献   

7.
舒世昌  刘三阳 《数学进展》2004,33(5):563-569
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。  相似文献   

8.
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。  相似文献   

9.
某些特殊曲面和子流形的等周不等式   总被引:3,自引:0,他引:3  
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  相似文献   

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We obtain the Omori-Yau maximum principle on complete properly immersed submanifolds with the mean curvature satisfying certain condition in complete Riemannian manifolds whose radial sectional curvature satisfies some decay condition, which generalizes our previous results in [17]. Using this generalized maximum principle, we give an estimate on the mean curvature of properly immersed submanifolds in H^n × R^e with the image under the projection on H^n contained in a horoball and the corresponding situation in hyperbolic space. We also give other applications of the generalized maximum principle.  相似文献   

12.
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.  相似文献   

13.
Given a family of smooth immersions of closed hypersurfaces in a locally symmetric Riemannian manifold with bounded geometry,moving by mean curvature flow,we show that at the first finite singular time of mean curvature flow,certain subcritical quantities concerning the second fundamental form blow up.This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao,but also extends the latest work of Le in the Euclidean case.  相似文献   

14.
THEGAUSSMAPOFTIMELIKESURFACESINR_1~n¥HONGJIANQIAOAbstract:Gaussmapsoforientedtimelike2-surfacesinarecharacterized,anditisshown...  相似文献   

15.
Let M be a complex analytic manifOld there is given a positive definite quadratic differentialform[1]dS2 = gjkdZJdZ* (1)where the Latin indices j, k take the values 1,2,' l n; 1, 2,' t n. Assume the Greek indices o, Ptake the value8 1,2,', n and.=. l cr if i= al = 1 cr if i= a, (2)t cr if i = cr.Assume now that the symmetric tensor gjk is selfadoint(see below Definitioll l), that is-- --gap = g95 = go0 = g9rr, (3)g.0 = gPcr = gap = g05. (4)and 8atisfiesgoP = gap = 0. (5)From the com…  相似文献   

16.
王琪 《数学杂志》2017,37(1):211-214
本文研究了双曲空间形式中等距浸入的紧致无边超曲面的全脐性质和高阶平均曲率.利用高阶平均曲率积分估计的方法,获得了一个新的定理,改进了这个研究方向上有关的最近结果.  相似文献   

17.
《偏微分方程通讯》2013,38(11-12):2513-2525
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.  相似文献   

18.
《代数通讯》2013,41(11):5513-5519
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.  相似文献   

19.
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.  相似文献   

20.
陈辉  黄慧 《系统科学与数学》2010,30(7):1026-1030
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.  相似文献   

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