共查询到20条相似文献,搜索用时 31 毫秒
1.
Basudeb Data 《Geometriae Dedicata》1998,73(2):143-155
A simplicial complex is said to satisfy complementarity if exactly one of each complementary pair of nonempty vertex-sets constitutes a simplex of the complex. In this article we show that if there exists a n-vertex d-dimensional pseudo-manifold M with complementarity and either nd+6 or d 6 then d = 0, 2, 4 or 6 with n = 3d/2 + 3. We also show that if M is a d-dimensional pseudo-manifold with complementarity and the number of vertices in M is d+5 then M is either a set of three points or the unique 6-vertex real projective plane or the unique 9-vertex complex projective plane. 相似文献
2.
要设(Mn,go)(n奇数)是紧Riemannian流形,λ(go)〉0,这里λ(go)是算子-4△go+R(go)的第一特征值,R(go)是(Mn,go)的数量曲率.设以(Mn,go)为初值的规范化的Ricci流的极大解g(t)满足|R(g(t))|≤C和λ(对某个常数C一致成立).我们证明这个解有子列收敛于一个Ricci收缩孤立子.进一步,当n=3时,条件fM |Rm(g(t))+n/2dμt ≤ C可去. 相似文献
3.
We introduce the adaptive neighborhood graph
as a data structure for modeling a smooth manifold M embedded in
some Euclidean space Rd. We assume that M is known to
us only through a finite sample P \subset M, as is often the
case in applications. The adaptive neighborhood graph is a geometric
graph on P. Its complexity is at most \min{2^{O(k)n, n2},
where n = |P| and k = dim M, as opposed to the n\lceil d/2
\rceil complexity of the Delaunay triangulation, which is often
used to model manifolds. We prove that we can correctly infer the
connected components and the dimension of M from the adaptive
neighborhood graph provided a certain standard sampling condition is
fulfilled. The running time of the dimension detection algorithm is
d2O(k^{7} log k) for each connected component of M. If the
dimension is considered constant, this is a constant-time operation,
and the adaptive neighborhood graph is of linear size. Moreover, the
exponential dependence of the constants is only on the intrinsic
dimension k, not on the ambient dimension d. This is of
particular interest if the co-dimension is high, i.e., if k is
much smaller than d, as is the case in many applications. The
adaptive neighborhood graph also allows us to approximate the
geodesic distances between the points in P. 相似文献
4.
Litan Yan 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):47-56
Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 . 相似文献
5.
6.
构造了一类步数为2(k+1)的次黎曼流形,给出其上连接原点和t轴上一点测地线的条数和相应测地线的长度,同时得到其中最短的测地线. 相似文献
7.
Xin Yuanlong 《数学年刊B辑(英文版)》1992,13(4):385-395
Let M be a compact Riemannian manifold of dimension m, N a complete Amply connected δ-pinched Riemannian manifold of dimension n. There exists a constant d(n). It is proved that if m≤d(n), then every minimizing map from M into N is smooth in the interior of M. If m=d(n)+1, such a map has at most diserete singular set and in general the Hausdorff dimension of the singular set is at most m-d(n)-1. 相似文献
8.
Yuguang ZHANG 《数学年刊B辑(英文版)》2007,28(4)
Compact K(a)hler manifolds with semi-positive Ricci curvature have been investigated by various authors. From Peternell's work, if M is a compact K(a)hler n-manifold with semi-positive Ricci curvature and finite fundamental group, then the universal cover has a decomposition (M) ≌ X1 × … × Xm, where Xj is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xj satisfies Ho(Xj,Ωp) = 0. The purpose of this paper is to generalize this theorem to almost non-negative Ricci curvature K(a)hler manifolds by using the Gromov-Hausdorff convergence. Let M be a compact complex n-manifold with non-vanishing Euler number. If for any ε > 0, there exists a K(a)hler structure (Je,ge) on M such that the volume Volge(M) < V, the sectional curvature |K(gε)| < Λ2, and the Ricci-tensor Ric(gε)> -εgε, where ∨ and Λ are two constants independent of ε. Then the fundamental group of M is finite, and M is diffeomorphic to a complex manifold X such that the universal covering of X has a decomposition, (X) ≌ X1 × … × Xs, where Xi is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xi satisfies Ho(Xi, Ωp) = {0}, p > 0. 相似文献
9.
1.IntroductionIn[1],Alavietal.gavethefollowingdecompositionconjecture.Conjecture.LetGbeagraphwith("1')edges.ThentheedgesetofGcanbedecomposedintonsetsgeneratinggraphsGI,G2,'IG.suchthatIE(Gi)I=i(fori=1,2,',n)andGiisisomorphictoasubgraphofGi 1fori=1,2,'.)n--1.AgraphGthatcanbedecomposedasdescribedinConjecturewillbesaidtohaveanAscendingSubgraphDecomposition(AlsoabbreviatedasASD).ThesubgraphsGIIG2,',G.aresaidtobemembersofsuchadecomposition.Furthermore,ifeachGiisastar(matching,pat… 相似文献
10.
SUBMANIFOLDS OF A HIGHER DIMENSIONAL SPHERE 总被引:1,自引:1,他引:0
Huang Xuanguo 《数学年刊B辑(英文版)》1983,4(1):33-40
Let M be an m-dimensional manifold immersed in S~(m+k)(r).Then △X=μH-(m/r~2)X,where X is the position vector of M and H is a unit normal vector field which is orthogonalto X everywhere.If M is a compact connected manifold with parallel mean curvature vector field ξimmersed inS~(m+k)(r),and the sectional curvature of M is not less than (1/2)((1/r~2)+|ξ|~2),thenM is a small sphere.For a compact connected hypersurface M in S~(m+1)(r),if the sectional curvature is non-nesative and the scalar curvature is proportional to the mean curvature everywhere,then M isa totally umbilical hypersurface or the multiplication of two totally umbilical submanifolds. 相似文献
11.
Roman Dwilewicz 《Annali di Matematica Pura ed Applicata》1985,139(1):15-43
Summary The main purpose of this paper is to give a sufficient condition for global embeddability of smooth Cauchy-Riemann manifolds (CR-manifolds) into complex manifolds with boundary. Namely, let M be a smooth CR-manifold of real dimension 2n – 1 and CR-dimension n – 1, where n 2, which is locally CR-embeddable into a complex manifold. Assume further that the Levi form of M is non-vanishing at each point. The main result of this paper is that such a CR-manifold is globally CR-embeddable into an n-dimensional complex manifold with boundary. Moreover if the Levi form has at each point of M eigenvalues of opposite signs, then M embeds into a complex manifold without boundary.This research is supported by a grant from Consiglio Nazionale delle Ricerche in Italy. 相似文献
12.
关于丛属函数的几个不等式 总被引:2,自引:0,他引:2
<正> 1.引言.设(?)是单位圆中的正则函数,函数w=F(z)将|z|<1映照成黎曼面S_F.设函数(?)在单位圆中是正则的.假如w=f(z)的一切函数值都落在 S_F,上,那末说 f(z)丛属于 F(z),记此关系为 f(z)(?)F(z).我们知道 f(z)(?)F(z)的充要条件是存在|z|<1上的正则函数ω(z),适合|ω(z)|<1,ω(0)=0,和 f(z)≡F(ω(z)). 相似文献
13.
LIU XIANGAO 《数学年刊B辑(英文版)》2002,23(1):119-136
61. IntroductionLet (M, g) be a compact smooth foemannian manifOld of dimension n with C2 boundary0M, and (N, h) be a smooth compact Riemannian manifolds of dimension k. Assume that(N, h) without boundary is isometrically embedded into the Euclidean space (Rm, (., .)).We assume that Sobolev spaceHl (M, N) = {u E Hl (M; R',.)lu(x) E N for a.e.x E M}and for every u E H1 (M; N), define the energy of u,E(u) = / lVuI'dv, (1.1)j. lVuI'dv, (1.1)where in local coordinate 1VuI' = g"pff 3, … 相似文献
14.
闭光滑流形上的奇异积分方程 总被引:12,自引:0,他引:12
<正> §1.前言 自Giraud G.以来,已有不少关于闭光滑流形上的奇异积分和奇异积分方程的研究(见[10]),但利用多复变函数的Cauchy型积分作为工具者,至今不多(如[3—8]),而在一维奇异积分方程论中,复变函数的Cauchy型积分起着基本的作用.本文试以定理在多复变函数论中的拓广为基础,讨论闭光滑流形上奇异积分的合成和奇异积分方程的求解,其方法和结论,都是与Giraud G.等人的工作全然不同的. 相似文献
15.
16.
Yu Xiang LI 《数学学报(英文版)》2006,22(2):545-550
We will show in this paper that if A is very close to 1, then
I(M,λ,m) =supu∈H0^1,n(m),∫m|△↓u|^ndV=1∫Ω(e^αn|u|^n/(n-1)-λm∑k=1|αnun/(n-1)|k/k!)dV
can be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" (Comm. Pure. Appl. Math., 55, 135-152, 2002). 相似文献
17.
设M ,V ,Q是李普希茨流形 ,M是V的局部LIP平坦的紧子流形 ,V是开流形且dimV =dimQ .设U是M在V中的某开邻域且Δn 是Rn 中n维标准单形 .如f:Δn×U→Δn×Q是一个LIP浸入且P1f =P1,称f是一个n维单形 .令 (IMV(m ,Q) ) n 是上面所定义的所有n维单形的集合且令IMV(m ,Q) ={ (IMV(M ,Q) ) n} n 0 .本文证明了IMV(M ,Q)在我们所定义的面运算 i和退化运算Si下是一个半单复形 . 相似文献
18.
设M是复流形,具有复(α,β)度量F=αφ(|β|/α),其中α为M上的Hermite度量,β为M上的(1,0)形式。本文得到与F相联系的复非线性联络系数Гiμ^i的表达式,且证明了:若β为M上的全纯(1,0)形式,并且关于α的Hermite联络γij^k(z)平行,则F是M上的复Berwald度量;若α是M上的Kaihler度量,则F是M上的强Kahler Finsler度量. 相似文献
19.
Let (V, U) be the vertex-partition of tree T as a bipartite graph. T is called an (m,n)-tree if |V|=m and |U| = n. For given positive integers m,n and d, the maximum spectral radius of all (m,n)-trees on diameter d are obtained, and all extreme graphs are determined. 相似文献
20.
單葉函數的係數(Ⅱ) 总被引:1,自引:1,他引:0
<正> §1.引言 在[1]文中,作者曾經對於單葉函數的係數進行討論,在本文中,將繼續之.在本文中所用的記號與[1]相同,不再一一重複定義,例如:記在單位圓|z|<1中k次對稱正则單葉函數的全體為S_k,特別記S_1,=S等等. 相似文献