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本文研究了Rn中平坦的外平行体的平均曲率积分.利用积分几何的方法和凸体理论的相关知识,得到了这些平均曲率积分的均值.作为推论,我们得到了这些平均曲率积分所对应的均质积分的均值. 相似文献
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§1.IntroductionLetNn+ppbean(n+p)-dimensionalconnectedpseudo-Riemannianmanifoldofindexp.IfNn+ppiscompleteandhasconstantsection... 相似文献
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1IntroductionTherehavebeensomeinterestingresultsinstudyingtheflowofconvexhypersurfacesintheEuclideanspacebyfunctionsOftheirprincipalcurvatures.BeingviewedasanextensionOfthetheoremOfGageandHedton[3],Huiskellprovedin16]thatdeformingconvexhypersurforesbytheirmeancurysturefunctiollsconvergetoaroundsphereinasense.FollowingthemethodsOfHuiskell[6]andTso[IOI,Chowshowedin[1]thatthesame.statementasin.[6]reconstrueifthemeancurvatureisreplacedbythen-throotoftheGauss-Kroneckercurvature.FOrgenerality… 相似文献
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本文研究了复射影空间中具有平行平均曲率向量的黎曼叶状结构(F).利用Nalcagawa 和Takagi的计算散度的方法,得到了复射影窄问中具有平行平均曲率向量的黎曼叶状结构(F)上向量场的散度,证明了其上的一个整体Pinching定理,从而将复射影空间中任何具有极小法平面场的调和叶的仵质推广到复射影窄间中具有平行平均曲率向量的黎曼叶状结构(F)上. 相似文献
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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
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郑权等在[1]-[3]中提出了一种求解无约束优化问题的均值算法,若假设目标函数f(x)是连续的,还讨论了均值算法的收敛性。若假设f(x) 有界闭集Ω上的凸函数,本文证明了求解凸函数极小值的均值算法是线性收敛的。 相似文献
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本文证明了一个拼嵌的爱因斯坦流形中的任何超曲面在沿其平均曲率向量演化时,如果初发始曲面满足保持其截曲率为正的某些条件,则在有限时间内超曲而将收缩成一点。 相似文献
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曲面上离散点集的光滑插值 总被引:1,自引:0,他引:1
本文主要解决了如下问题:给定R3凸曲面上的任意个离散点{Pi}Ni=1及其对应的函数值{fi}Ni=1,要求构造曲面上的插值函数f(x),使得f(Pi)=fi,(i=1,2,…,N).本文方法推广了球面上离散点集的Multiquadric插值方法,并且对分区域插值方法也给予了讨论. 相似文献
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In this article, we prove that the double inequality
αP(a,b)+(1-α)Q(a,b)〈M(a,b)〈βP(a,b)+(1-β)Q(a,b)
holds for any a,b 〉 0 with a ≠ b if and only if α≥1/2 and β≤[π(√2 lov (1+√2)-1]/[√2π-2) log (1+√2)]=0.3595…,where M(a, b), Q(a, b), and P(a, b) ave the Neuman-Sandor, quadratic, and first Seiffert means of a and b, respectively. 相似文献
αP(a,b)+(1-α)Q(a,b)〈M(a,b)〈βP(a,b)+(1-β)Q(a,b)
holds for any a,b 〉 0 with a ≠ b if and only if α≥1/2 and β≤[π(√2 lov (1+√2)-1]/[√2π-2) log (1+√2)]=0.3595…,where M(a, b), Q(a, b), and P(a, b) ave the Neuman-Sandor, quadratic, and first Seiffert means of a and b, respectively. 相似文献
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61. IntroductionLet P be a submanifold of an n-dimensional riemannian manifold AI. Expressions fOrthe kth integrated mean curvatures, M^P(t), (i. e. the integral of tho kth mcan curvature,k = 0, 1,' l n -- l), of a tubular hypersurface P of radius t about P, in terms of theRiemann curvature tensor of P. are calculated when AI is Euclidean or a rank one symmetricspace[5'13"1. Moreover, when P is a closed convex hypersurface of thc n-dimensional spaceof constant curvature A', Santal6 has… 相似文献
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1IntroductionInthispaper,wewillconsiderthebehavinrOfparallelmultiplicativeiterativemethodsfortheconstrainedopt~ationproblemwhereIisaconvexcontinuouslydtherentiablefunctiononR;withcompactlevelsetsandlOCallyLiP8chitzcontinuousgradient.In[1]Eggerinontintroducedapracticalapprodriatemethodforsolving(1,1),theresultingalgorithmhastheformwhereVI(x*)isthegradientofl(:)atac,andwbisarelaxation/steplengthparameter,andinwhichMisanarbitrarylfordconstant,andListheLipschitzconstantofVI(x),thatistosaylth… 相似文献
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In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed. 相似文献
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吴加勇 《数学物理学报(B辑英文版)》2013,33(1):171-186
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