共查询到20条相似文献,搜索用时 15 毫秒
1.
Let (M, g) be an n-dimensional compact and connected Riemannian manifold of constant scalar curvature. If the sectional curvatures
of M are bounded below by a constant α > 0, and the Ricci curvature satisfies Ric < (n − 1)αδ, δ ≥ 1, then it is shown that
either M is isometric to the n-sphere Sn(α) or else each nonzero eigenvalue λ of the Laplacian acting on the smooth functions of M satisfies the following:
. 相似文献
2.
An important problem in the study of Ricci flow is to find the weakest conditions that provide control of the norm of the
full Riemannian curvature tensor. In this article, supposing (M
n
, g(t)) is a solution to the Ricci flow on a Riemmannian manifold on time interval [0, T), we show that
L\fracn+22{L^\frac{n+2}{2}} norm bound of scalar curvature and Weyl tensor can control the norm of the full Riemannian curvature tensor if M is closed and T < ∞. Next we prove, without condition T < ∞, that C
0 bound of scalar curvature and Weyl tensor can control the norm of the full Riemannian curvature tensor on complete manifolds.
Finally, we show that to the Ricci flow on a complete non-compact Riemannian manifold with bounded curvature at t = 0 and with the uniformly bounded Ricci curvature tensor on M
n
× [0, T), the curvature tensor stays uniformly bounded on M
n
× [0, T). Hence we can extend the Ricci flow up to the time T. Some other results are also presented. 相似文献
3.
Song Bo Hou 《数学学报(英文版)》2011,27(10):1935-1940
Let (M,g(t)), 0 ≤ t ≤ T, be an n-dimensional closed manifold with nonnegative Ricci curvature, |Rc| ≤ C/t for some constant C > 0 and g(t) evolving by the Ricci flow
$\frac{{\partial g_{ij} }}
{{\partial t}} = - 2R_{ij} .
$\frac{{\partial g_{ij} }}
{{\partial t}} = - 2R_{ij} .
相似文献
4.
Dan Mangoubi 《Mathematische Annalen》2008,341(1):1-13
We consider Riemannian metrics compatible with the natural symplectic structure on T
2 × M, where T
2 is a symplectic 2-torus and M is a closed symplectic manifold. To each such metric we attach the corresponding Laplacian and consider its first positive
eigenvalue λ1. We show that λ1 can be made arbitrarily large by deforming the metric structure, keeping the symplectic structure fixed. The conjecture is
that the same is true for any symplectic manifold of dimension ≥ 4. We reduce the general conjecture to a purely symplectic
question. 相似文献
5.
Wel Dong LIU Zheng Yan LIN 《数学学报(英文版)》2008,24(1):59-74
Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2(log2{X})^2〈∞and φ(n)=O(1/log n)^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O(√n/(log2n)^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP(|Sn|≥ε√ESn^2log2n+an)=√2.The results of Gut and Spataru (2000) are special cases of ours. 相似文献
6.
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete
(not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general
metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric
g
≥−(n−1)a
2, a≥0, then there exist constants A
n
>0,B
n
>0 only depending on the dimension, such that
7.
In this paper, we study complete Riemannian n-manifolds (n ≥ 3) with asymptotically nonnegative Ricci curvature and weak bounded geometry. We show among other things that the total
Betti number of such a manifold has polynomial growth of degree n
2 + n. Further more, such a manifold is of finite topological type if the volume growth rate of the metric ball around the base
point is less than
This work is partly supported by the National Natural Science Foundation (10371047) of China.
Received: 13 June 2006 相似文献
8.
Sharp estimates for the Ricci curvature of a submanifold M
n
of an arbitrary Riemannian manifold N
n+p
are established. It is shown that the equality in the lower estimate of the Ricci curvature of M
n
in a space form N
n+p
(c) is achieved only when M
n
is quasiumbilical with a flat normal bundle. In the case when the codimension p satisfies 1 ≤ p ≤ n − 3, the only submanifolds in N
n+p
(c) on which the Ricci curvature is minimal are the conformally flat ones with a flat normal bundle.
相似文献
9.
Using Hamilton's Ricci flow we shall prove several pinching results for integral curvature. In particular, we show that if
p>n/2$ and the L
p
norm of the curvature tensor is small and the diameter is bounded, then the manifold is an infra-nilmanifold. We also obtain
a result on deforming metrics to positive sectional curvature.
Received: 17 February 1999 相似文献
10.
Let (X, Xn; n ≥1) be a sequence of i.i.d, random variables taking values in a real separable Hilbert space (H, ||·||) with covariance operator ∑. Set Sn = X1 + X2 + ... + Xn, n≥ 1. We prove that, for b 〉 -1,
lim ε→0 ε^2(b+1) ∞ ∑n=1 (logn)^b/n^3/2 E{||Sn||-σε√nlogn}=σ^-2(b+1)/(2b+3)(b+1) B||Y|^2b+3 holds if EX=0,and E||X||^2(log||x||)^3bv(b+4)〈∞ where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator ∑, and σ^2 denotes the largest eigenvalue of ∑. 相似文献 11.
We prove the following extension of the Wiener–Wintner theorem and the Carleson theorem on pointwise convergence of Fourier
series: For all measure-preserving flows (X,μ,T
t
) and f∈L
p
(X,μ), there is a set X
f
⊂X of probability one, so that for all x∈X
f
,
12.
E.G. Coffman Jr. George S. Lueker Joel Spencer Peter M. Winkler 《Probability Theory and Related Fields》2001,120(4):585-599
A random rectangle is the product of two independent random intervals, each being the interval between two random points
drawn independently and uniformly from [0,1]. We prove that te number C
n
of items in a maximum cardinality disjoint subset of n random rectangles satisfies
13.
Brian Curtin 《Graphs and Combinatorics》1999,15(2):143-158
Let Γ=(X,E) denote a bipartite distance-regular graph with diameter D≥4, and fix a vertex x of Γ. The Terwilliger algebra
T=T(x) is the subalgebra of Mat
X(C) generated by A, E
*
0, E
*
1,…,E
*
D, where A denotes the adjacency matrix for Γ and E
*
i denotes the projection onto the i
TH subconstituent of Γ with respect to x. An irreducible T-module W is said to be thin whenever dimE
*
i
W≤1 for 0≤i≤Di. The endpoint of W is min{i|E
*
i
W≠0}.
We determine the structure of the (unique) irreducible T-module of endpoint 0 in terms of the intersection numbers of Γ. We show that up to isomorphism there is a unique irreducible
T-module of endpoint 1 and it is thin. We determine its structure in terms of the intersection numbers of Γ. We determine the
structure of each thin irreducible T-module W of endpoint 2 in terms of the intersection numbers of Γ and an additional real parameter ψ=ψ(W), which we refer to as the type of W.
We now assume each irreducible T-module of endpoint 2 is thin and obtain the following two-fold result. First, we show that the intersection numbers of Γ
are determined by the diameter D of Γ and the set of ordered pairs
14.
Katalin Gyarmati 《The Ramanujan Journal》2008,17(3):387-403
Let τ(n) be the number of positive divisors of an integer n, and for a polynomial P(X)∈ℤ[X], let
15.
Klaudiusz Wójcik 《Monatshefte für Mathematik》2002,135(3):245-252
We prove a sufficient condition for the existence of 2
n
(geometrically distinct) solutions of the two point boundary value problem
16.
Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0, 1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points, then (↓USCC(X), ↓CC(X)) ≈ (Q, c0 ∪ (Q \ Σ)), i.e., there is a homeomorphism h :↓USCC(X) → Q such that h(↓CC(X)) = c0 ∪ (Q \ Σ... 相似文献
17.
Let S be the multiplicative semigroup of q×q matrices with positive entries such that every row and every column contains a strictly positive element. Denote by (X
n
)
n≥1 a sequence of independent identically distributed random variables in S and by X
(n)=X
n
⋅⋅⋅
X
1, n≥1, the associated left random walk on S. We assume that (X
n
)
n≥1 satisfies the contraction property
18.
Let α? (1,2) and X
α
be a symmetric α-stable (S α S) process with stationary increments given by the mixed moving average
19.
Ezio Araujo Costa 《Archiv der Mathematik》2005,85(2):183-189
Let Mn be a complete Riemannian manifold immersed isometrically in the unity Euclidean sphere
In [9], B. Smyth proved that if Mn, n ≧ 3, has sectional curvature K and Ricci curvature Ric, with inf K > −∞, then sup Ric ≧ (n − 2) unless the universal covering
of Mn is homeomorphic to Rn or homeomorphic to an odd-dimensional sphere. In this paper, we improve the result of Smyth. Moreover, we obtain the classification of complete hypersurfaces of
with nonnegative sectional curvature.Received: 11 November 2003 相似文献
20.
In the article [2] Ennio De Giorgi conjectured that any compact n-dimensional regular submanifold M of ℝ
n+m
,moving by the gradient of the functional
|