共查询到18条相似文献,搜索用时 62 毫秒
1.
1IntroductionLetiM.g)beac0mpactn-dimensi0nd1Riemannianmanffold.ByAwedenotetheLaplacianartingonpf0rnaonM.Thenwehavethespectrumforeachp:Oneoftlieprob1emonspectraisasf0110ws:Let(M,g)and(M,g)becompactoritabieRicmannianmanif01dswithSpecp(M.g)=Specp{M-g),thenis(M,g)isometricto(M-j)?Thisprob1emisprovedtobewrongbyJ.Milnorin1964.Butwhen(M,g)and(M.g)aresonlespecialffiemannianmanifolds.undercertainconditi0ns.wecanprovethat(M.g)'sisometricto{M.j).Foran-din1ensi0nsubmanitbldMinSN,wedenotetheleng… 相似文献
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In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω. 相似文献
3.
Let M be a Kahler manifold of complex dimensions m and Z_I,…,Z_m.be mcomplex vectors which form a frame in the neighbourhood of a point p∈M andω~1,…,ω~m be the dual coframe.Denote ds~2=h_αβ~(ω~αω~β) 相似文献
4.
1. IntroductionLet G be a simple graph with vertex set V = {yi, v2,'', v.} and edge set E ~ E(G).Denote the degree of vertex yi by di. Let D(G) ~ diag (dl, d2,'', da) and A(G) be thediagonal mains of vertex degrees and the adjacency matrix of G, respectively. Then L(G) D(G)-A(G) is the Laplacian matrix of G. It seems that L(G) first occurred in the celebratedMatriX-Thee Theorem:Theorem 1.1. If Li j is the submatrix of L(G) obtained by deleting its i-th row andj-th column, then (-… 相似文献
5.
张恭庆 《数学物理学报(B辑英文版)》1991,(3)
Given a C~2-function f on a Hilbedrt Riemannian manifold M, let ∑ be a. nondegonerate critical manifold of f, what becomes of ∑, if we perturbe f to f+g? When g is a C~2 perturbation, i.e. ||g||c~2 is small, there was a result due to M. Reeken by the inverse function theorem. It was rediscovered by Ambrosetti et. 相似文献
6.
In this paper, we use a kind of main part symmetry scheme to study the center manifolds and Hop f bifurcations for ODEs, and set up a kind of method for calculation them. 相似文献
7.
In[4],Li proved that Yau's conjecture“For non-compact connected completeRiemannian manifold M.M has no L~2-eigenvalues if its sectional curvature K_m≥0”holds if M can be represented as a Riemannian product M=R~1×N.Acturally,heproved(without the restriction K_m≥0) 相似文献
8.
陈晓漫 《数学年刊B辑(英文版)》1989,(4)
In this paper, it is shown that, for a contraction on π_k, the intersection of its spectrum with the exterior of the unit disk is a finite set of isolated eigenvalues, each of which has finite multplicity. Futhermore some relations between its spectrum and the spectrum of its minimal unitary dilation are established. 相似文献
9.
In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kahler manifolds with certain nonnegative holomorphic bisectional curvature and sectional curvature is at least half of the real dimension. The authors also give a brief proof of a generalized Yau's theorem. 相似文献
10.
We introduce four types of special eigenvalues which lie on the boundary of certain inclusion regions for the spectrum of a complex square matrix, i.e. , R_r(G_c)-,O(a)-,B_r(B_c)-. and OB(a)- eigenvalues. Then we characterize these eigenvalues and their corresponding eigenvectors for irreducible matrices, Finally we give some new sufficient conditions for an irreducible complex matrix to be nonsingular. 相似文献
11.
设M2m+1(K)是Zn+1维常ψ一截面曲率K的紧致Sasaki流形,本文证明了与M2m+1(K)等谱的上同调Einstein的紧致Sasaki流形必有常ψ-截面曲率K. 相似文献
12.
极小超曲面上Laplace算子的谱 总被引:1,自引:0,他引:1
本文证明了单位球面S^n+1中某些Clifford超曲面,复射影空间和四元数射影空间中广YQ LIFFORDFHV MA DM J MH ADW H Laplace算子的谱唯一确定。 相似文献
13.
本文证明了Heisenberg群上Laplace算子的Dirichlet特征值的存在性,给出了特征值的估计 相似文献
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15.
本文首先对流形的测地球上的Sobolev常数进行讨论,并利用它进行Moser迭代,最终得到具有小负曲率的闭的黎曼流形上Laplace算子特征值的一个下界估计. 相似文献
16.
本文研究了黎曼流形上Laplace算子的第一特征值,利用流形的测地球上的Sobolev常数进行讨论并进行Moser迭代,得到闭的黎曼流形上Laplace算子第一特征值的一个下界估计. 相似文献
17.
本文研究了连通图的Laplacian特征值,利用图的Laplacian矩阵的特征多项式的行列式表示式,对存在两个不同顶点,但有相同邻集的一类图,得到了一个Laplacian特征值,并给出了它的应用. 相似文献