共查询到20条相似文献,搜索用时 15 毫秒
1.
Danny Calegari 《Geometric And Functional Analysis》2008,18(1):50-76
This paper establishes the existence of a gap for the stable length spectrum on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive ϵ there is a positive δ depending only on n and on ϵ such that an element of π1(M) with stable commutator length less than δ is represented by a geodesic with length less than ϵ. Moreover, for any such M, the first accumulation point for stable commutator length on conjugacy classes is at least 1/12.
Conversely, “most” short geodesics in hyperbolic 3-manifolds have arbitrarily small stable commutator length. Thus stable
commutator length is typically good at detecting the thick-thin decomposition of M, and 1/12 can be thought of as a kind of
homological Margulis constant.
Received: June 2006 Revision: May 2007 Accepted: June 2007 相似文献
2.
Hitoshi Tanaka 《数学学报(英文版)》2002,18(3):447-454
Let K
δ, 0 < δ≪1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity δ. The (so-called)
Fefferman-Stein-type inequality: is shown, where C
d
and α
d
are constants depending only on the dimension d and w is a weight. The result contains the exponent (d−2)/2d which is smaller than the exponent (d−2)(d−1)/d(2d−3) obtained in [7].
Received October 8, 2001, Accepted February 28, 2002 相似文献
3.
We study self adjoint operators of the form?H
ω = H
0 + ∑λω(n) <δ
n
,·>δ
n
,?where the δ
n
’s are a family of orthonormal vectors and the λω(n)’s are independently distributed random variables with absolutely continuous probability distributions. We prove a general
structural theorem saying that for each pair (n,m), if the cyclic subspaces corresponding to the vectors δ
n
and δ
m
are not completely orthogonal, then the restrictions of H
ω to these subspaces are unitarily equivalent (with probability one). This has some consequences for the spectral theory of
such operators. In particular, we show that “well behaved” absolutely continuous spectrum of Anderson type Hamiltonians must
be pure, and use this to prove the purity of absolutely continuous spectrum in some concrete cases.
Oblatum 27-V-1999 & 6-I-2000?Published online: 8 May 2000 相似文献
4.
Michael Stoll 《Inventiones Mathematicae》1996,126(1):85-109
This paper considers growth series of 2-step nilpotent groups with infinite cyclic derived subgroup. Every such group G has a subgroup of finite index of the form H
n
×ℤ
m
, where H
n
is the discrete Heisenberg group of length 2n+1. We call n the Heisenberg rank of G.
We show that every group of this type has some finite generating set such that the corresponding growth series is rational.
On the other hand, we prove that if G has Heisenberg rank n ≧ 2, then G possesses a finite generating set such that the corresponding growth series is a transcendental power series.
Oblatum 1-III-1995 & 28-XII-1995 相似文献
5.
Bertram A.F. Wehrfritz 《Central European Journal of Mathematics》2011,9(3):616-626
Let ϕ be an automorphism of prime order p of the group G with C
G
(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are bounded in terms of p, n and h only. Here a group has finite Hirsch number if it is poly (cyclic or locally finite). This is a stronger notion than that
used in [Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)], where the
case p = 2 is discussed. 相似文献
6.
E. Rips 《Israel Journal of Mathematics》1981,39(3):186-188
This note presents an example that disproves, forn=4, Weinbaum’s conjecture, that ifw is a cyclically reduced primitive word inF
n
such that all the generatorsx∈X appear inw then some cyclic permutation ofw can be partitioned inton words generatingF
n
:w≡uv,vu≡s
1
s
2…s
n
, <s
1,s
2,…s
n
>=F
n
. 相似文献
7.
A new proof of a theorem by Gromov is given: for any positive C and any integer n greater than 1, there exists a function Δ
C,n
(δ) such that if the Gromov–Hausdorff distance between two complete Riemannian n-manifolds V and W is at most δ, their sectional curvaturcs |K
σ
| do not exceed C, and their injectivity radii are at least 1/C, than the Lipschitz distance between V and W is less than Δ
C,n
(δ), and Δ
C,n
(δ) → 0 as δ → 0. Bibliography: 6 titles. 相似文献
8.
We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S n+1 satisfying Sf 4 f_3~2 ≤ 1/n S~3 , where S is the squared norm of the second fundamental form of M, and f_k =sum λ_i~k from i and λ_i (1 ≤ i ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n + δ(n), then S ≡ n, i.e., M is one of the Clifford torus S~k ((k/n)~1/2 ) ×S~... 相似文献
9.
The Ramsey number r(H, K
n
) is the smallest positive integer N such that every graph of order N contains either a copy of H or an independent set of size n. The Turán number ex(m, H) is the maximum number of edges in a graph of order m not containing a copy of H. We prove the following two results: (1) Let H be a graph obtained from a tree F of order t by adding a new vertex w and joining w to each vertex of F by a path of length k such that any two of these paths share only w. Then r(H,Kn) £ ck,t [(n1+1/k)/(ln1/k n)]{r(H,K_n)\leq c_{k,t}\, {n^{1+1/k}\over \ln^{1/k} n}} , where c
k,t
is a constant depending only on k and t. This generalizes some results in Li and Rousseau (J Graph Theory 23:413–420, 1996), Li and Zang (J Combin Optim 7:353–359,
2003), and Sudakov (Electron J Combin 9, N1, 4 pp, 2002). (2) Let H be a bipartite graph with ex(m, H) = O(m
γ
), where 1 < γ < 2. Then r(H,Kn) £ cH ([(n)/(lnn)])1/(2-g){r(H,K_n)\leq c_H ({n\over \ln n})^{1/(2-\gamma)}}, where c
H
is a constant depending only on H. This generalizes a result in Caro et al. (Discrete Math 220:51–56, 2000). 相似文献
10.
Given a simplicial complex δ on vertices {1, …,n} and a fieldF we consider the subvariety of projective (n−1)-space overF consisting of points whose homogeneous coordinates have support in δ. We give a simple rational expression for the zeta function
of this singular projective variety overF
q and show a close connection with the Betti numbers of the corresponding variety over ℂ. This connection is particularly simple
in the case when Δ is Cohen-Macaulay. 相似文献
11.
Let ∑
n
−1 be the unit sphere in the n-dimensional Euclidean space ℝ
n
. For a funcion ƒ∈L(∑
n
−1) denote by σδ
N
(ƒ) the Cesàro means of order δ of the Fourier-Laplace series of ƒ. The special value of δ is known as the critical index. In the case when n is even, this paper proves the existence of the ‘rare’ sequence {n
k
} such that the summability
takes place at each Lebesgue point satisfying some antipole conditions.
Received June 28, 1999, Revised August 11, 1999, Accepted February 16, 2000 相似文献
12.
Recently, B. Y. Chen introduced a new intrinsic invariant of a manifold, and proved that everyn-dimensional submanifold of real space formsR
m
(ε) of constant sectional curvature ε satisfies a basic inequality δ(n
1,…,n
k
)≤c(n
1,…,n
k
)H
2+b(n
1,…,n
k
)ε, whereH is the mean curvature of the immersion, andc(n
1,…,n
k
) andb(n
1,…,n
k
) are constants depending only onn
1,…,n
k
,n andk. The immersion is calledideal if it satisfies the equality case of the above inequality identically for somek-tuple (n
1,…,n
k
). In this paper, we first prove that every ideal Einstein immersion satisfyingn≥n
1+…+n
k
+1 is totally geodesic, and that every ideal conformally flat immersion satisfyingn≥n
1+…+n
k
+2 andk≥2 is also totally geodesic. Secondly we completely classify all ideal semi-symmetric hypersurfaces in real space forms.
The author was supported by the NSFC and RFDP. 相似文献
13.
Chih-Wen Weng 《Graphs and Combinatorics》1998,14(3):275-304
Let Γ=(X,R) denote a distance-regular graph with diameter D≥2 and distance function δ. A (vertex) subgraph Ω⊆X is said to be weak-geodetically closed whenever for all x,y∈Ω and all z∈X,
We show that if the intersection number c
2>1 then any weak-geodetically closed subgraph of X is distance-regular. Γ is said to be i-bounded, whenever for all x,y∈X at distance δ(x,y)≤i,x,y are contained in a common weak-geodetically closed subgraph of Γ of diameter δ(x,y). By a parallelogram of length i, we mean a 4-tuple xyzw of vertices in X such that δ(x,y)=δ(z,w)=1, δ(x,w)=i, and δ(x,z)=δ(y,z)=δ(y,w)=i−1. We prove the following two theorems.
Theorem 1.
LetΓdenote a distance-regular graph with diameter
D≥2, and assume the intersection numbers
c
2>1, a
1≠0. Then for each integer i (1≤i≤D), the following (i)–(ii) are equivalent.
(i)*Γis i-bounded.
(ii)*Γcontains no parallelogram of length≤i+1.
Restricting attention to the Q-polynomial case, we get the following stronger result.
Theorem 2.
Let Γ denote a distance-regular graph with diameter D≥3, and assume the intersection numbers c
2>1, a
1≠0. Suppose Γ is Q-polynomial. Then the following (i)–(iii) are equivalent.
(i)*Γcontains no parallelogram of length 2 or 3.
(ii)*Γis D-bounded.
(iii)*Γhas classical parameters (D,b,α,β), and either
b<−1, or elseΓis a dual polar graph or a Hamming graph.
Received: February 8, 1995 / Revised: November 8, 1996 相似文献
14.
J. C. Gómez-Larrañaga F. González-Acuña Wolfgang Heil 《Mathematische Zeitschrift》2008,259(2):419-432
A closed topological n-manifold M
n
is of S
1-category 2 if it can be covered by two open subsets W
1,W
2 such that the inclusions W
i
→ M
n
factor homotopically through maps W
i
→ S
1 → M
n
. We show that the fundamental group of such an n-manifold is a cyclic group or a free product of two cyclic groups with nontrivial amalgamation. In particular, if n = 3, the fundamental group is cyclic.
相似文献
15.
Shiri Artstein-Avidan Omer Friedland Vitali Milman Sasha Sodin 《Israel Journal of Mathematics》2006,156(1):141-155
We present a quantitative form of the result of Bai and Yin from [2], and use to show that the section of ℓ
1
(1+δ)n
spanned byn random independent sign vectors is with high probability isomorphic to euclidean with isomorphism constant polynomial in
δ−1.
Partially supported by BSF grant 2002-006.
Supported by the National Science Foundation under agreement No. DMS-0111298.
Supported in part by the Israel Science Academy. 相似文献
16.
Let n ≥ 2 be a fixed positive integer, q ≥ 3 and c be two integers with (n, q) = (c, q) = 1. We denote by rn(51, 52, C; q) (δ 〈 δ1,δ2≤ 1) the number of all pairs of integers a, b satisfying ab ≡ c(mod q), 1 〈 a ≤δ1q, 1 ≤ b≤δ2q, (a,q) = (b,q) = 1 and nt(a+b). The main purpose of this paper is to study the asymptotic properties of rn (δ1, δ2, c; q), and give a sharp asymptotic formula for it. 相似文献
17.
We prove a general theorem on the zeros of a class of generalised Dirichlet series. We quote the following results as samples.
Theorem A.Let 0<θ<1/2and let {a
n
}be a sequence of complex numbers satisfying the inequality
for N = 1,2,3,…,also for n = 1,2,3,…let α
n
be real and |αn| ≤ C(θ)where C(θ) > 0is a certain (small)constant depending only on θ. Then the number of zeros of the function
in the rectangle (1/2-δ⩽σ⩽1/2+δ,T⩽t⩽2T) (where 0<δ<1/2)is ≥C(θ,δ)T logT where C(θ,δ)is a positive constant independent of T provided T ≥T
0(θ,δ)a large positive constant.
Theorem B.In the above theorem we can relax the condition on a
n
to
and |aN| ≤ (1/2-θ)-1.Then the lower bound for the number of zeros in (σ⩾1/3−δ,T⩽t⩽2T)is > C(θ,δ) Tlog T(log logT)-1.The upper bound for the number of zeros in σ⩾1/3+δ,T⩽t⩽2T) isO(T)provided
for every ε > 0.
Dedicated to the memory of Professor K G Ramanathan 相似文献
18.
Domingo Pestana José M. Rodríguez José M. Sigarreta María Villeta 《Central European Journal of Mathematics》2012,10(3):1141-1151
If X is a geodesic metric space and x
1; x
2; x
3 ∈ X, a geodesic triangle T = {x
1; x
2; x
3} is the union of the three geodesics [x
1
x
2], [x
2
x
3] and [x
3
x
1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity constant of cubic graphs (graphs with all of their vertices of
degree 3), and prove that for any graph G with bounded degree there exists a cubic graph G* such that G is hyperbolic if and only if G* is hyperbolic. Moreover, we prove that for any cubic graph G with n vertices, we have δ(G) ≤ min {3n/16 + 1; n/4}. We characterize the cubic graphs G with δ(G) ≤ 1. Besides, we prove some inequalities involving the hyperbolicity constant and other parameters for cubic graphs. 相似文献
19.
Rémi Vaillancourt 《Israel Journal of Mathematics》1972,13(1-2):225-231
This lecture gives an inside look into the proof of the continuity of pseudo-differential operators of orderm and typep, δ1, δ2 for 0≦p≦δ1=1, 0≦p≦δ2<1, andm/n≦p≦(δ1+δ2)/2. Applications are mentioned. 相似文献
20.
Menachem Kojman 《Israel Journal of Mathematics》2001,121(1):85-91
We present an ordinal rank, δ3, which refines the standard classification of non-convexity among closed planar sets. The class of closed planar sets falls
into a hierarchy of order type ω1 + 1 when ordered by δ-rank.
The rank δ3 (S) of a setS is defined by means of topological complexity of 3-cliques in the set. A 3-clique in a setS is a subset ofS all of whose unordered 3-tuples fail to have their convex hull inS. Similarly, δn (S) is defined for alln>1.
The classification cannot be done using δ2, which considers only 2-cliques (known in the literature also as “visually independent subsets”), and in dimension 3 or higher
the analogous classification is not valid. 相似文献