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1.
We show that if a hyperbolic 3-manifold M has two toroidal Dehn fillings with distance at least 3, then ∂M consists of at most three tori. As a result, we can obtain an optimal estimate for the number of exceptional slopes on hyperbolic
3-manifolds with boundary a union of at least 4 tori.
S. Lee was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion
Fund) (KRF-2007-314-C00024). M. Teragaito was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific
Research (C), 19540089. 相似文献
2.
In this paper we will present two upper estimates for the smallest area of a possibly singular minimal surface in a closed
Riemannian manifold Mn with a trivial first homology group. The first upper bound will be in terms of the diameter of Mn, the second estimate will be in terms of the filling radius of a manifold, leading also to the estimate in terms of the volume
of Mn. If n = 3 our upper bounds are for the smallest area of a smooth embedded minimal surface. After that we will establish similar
upper bounds for the smallest volume of a stationary k-dimensional integral varifold in a closed Riemannian manifold Mn with
. The above results are the first results of such nature.
Received: October 2004 Revision: May 2005 Accepted: June 2005 相似文献
3.
Let M and N be two r×r matrices of full rank over a discrete valuation ring R with residue field of characteristic zero. Let P,Q and T be invertible r×r matrices over R. It is shown that the orbit of the pair (M,N) under the action (M,N)?(PMQ-1,QNT-1) possesses a discrete invariant in the form of Littlewood-Richardson fillings of the skew shape λ/μ with content ν, where μ is the partition of orders of invariant factors of M, ν is the partition associated to N, and λ the partition of the product MN. That is, we may interpret Littlewood-Richardson fillings as a natural invariant of matrix pairs. This result generalizes invariant factors of a single matrix under equivalence, and is a converse of the construction in Appleby (1999) [1], where Littlewood-Richardson fillings were used to construct matrices with prescribed invariants. We also construct an example, however, of two matrix pairs that are not equivalent but still have the same Littlewood-Richardson filling. The filling associated to an orbit is determined by special quotients of determinants of a matrix in the orbit of the pair. 相似文献
4.
We show that if a closed manifold M admits an ℱ-structure (not necessarily polarized, possibly of rank zero) then its minimal entropy vanishes. In particular,
this is the case if M admits a non-trivial S
1-action. As a corollary we obtain that the simplicial volume of a manifold admitting an ℱ-structure is zero.?We also show
that if M admits an ℱ-structure then it collapses with curvature bounded from below. This in turn implies that M collapses with bounded scalar curvature or, equivalently, its Yamabe invariant is non-negative.?We show that ℱ-structures
of rank zero appear rather frequently: every compact complex elliptic surface admits one as well as any simply connected closed
5-manifold.?We use these results to study the minimal entropy problem. We show the following two theorems: suppose that M is a closed manifold obtained by taking connected sums of copies of S
4, ℂP
2,
2,S
2×S
2and the K3 surface. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
4,ℂP
2,S
2×S
2,ℂP
2#
2 or ℂP
2# ℂP
2. Finally, suppose that M is a closed simply connected 5-manifold. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
5,S
3×S
2, then on trivial S
3-bundle over S
2 or the Wu-manifold SU(3)/SO(3).
Oblatum 13-III-2002 & 12-VIII-2002?Published online: 8 November 2002
G.P. Paternain was partially supported by CIMAT, Guanajuato, México.?J. Petean is supported by grant 37558-E of CONACYT. 相似文献
5.
Jean Bertoin 《Probability Theory and Related Fields》1997,108(4):559-571
Summary. Given a closed Markov (i.e. regenerative) set in [0,∞), we characterize the laws of the Markov sets which are regeneratively
embedded into the latter. Typically, let Φ(1) and Φ(2) be two Laplace exponents corresponding to two regenerative laws, and M
(2) a Markov set with exponent Φ(2). There exists a Markov set M
(1) with exponent Φ(1) which is regeneratively embedded into M
(2) if and only if Φ(1)/Φ(2) is a completely monotone function. Several examples and applications are discussed.
Received: 12 April 1996 / In revised form: 12 March 1997 相似文献
6.
Chiteng'a John Chikunji 《代数通讯》2013,41(10):5049-5081
In [7], Corbas determined all finite rings in which the product of any two zero-divisors is zero, and showed that they are of two types, one of characteristic p 2and the other of characteristic p2. The purpose of this paper is to address the problem of the classification of finite rings such that. (i)the set of all zero-divisors form an ideal M. (ii)M 3=(0); and. (iii)M 3≠(0). Because of (i), these rings are called completely primary and we shall call a finite completely primary ring R which satisfies conditions (i), (ii) and (iii), a ring with property(T). These rings are of three types, namely, of characteristic p p 2 and p 3. The characteristic p 2 case is subdivided into cases in which p?M 2 p?ann(M)?M 2 and p?M ?ann(M), where ann(M) denotes the two-sided annihilator of where M in R. 相似文献
7.
Lu Fangyan 《高校应用数学学报(英文版)》1997,12(4):441-446
ESTIMATEFORDISTANCE┐COEFFICIENTOFMATRICESLUFANGYANAbstract.MotivationofthispaperisanopenproblemexposedbyB.Beauzamy[1].LetMbea... 相似文献
8.
The complex two-plane Grassmannian G
2(C
m+2
in equipped with both a K?hler and a quaternionic K?hler structure. By applying these two structures to the normal bundle
of a real hypersurface M in G
2(C
m+2
one gets a one- and a three-dimensional distribution on M. We classify all real hypersurfaces M in G
2
C
m+2
, m≥3, for which these two distributions are invariant under the shape operator of M.
Received 13 November 1996; in revised form 3 March 1997 相似文献
9.
It is shown that every H
-group G of type admits a finite dimensional G-CW-complex X with finite stabilizers and with the additional property that for each finite subgroup H, the fixed point subspace X
H
is contractible. This establishes conjecture (5.1.2) of [9]. The construction of X involves joining a family of spaces parametrized by the poset of non-trivial finite subgroups of G and ultimately relies on the theorem of Cornick and Kropholler that if M is a -module which is projective as a -module for all finite then M has finite projective dimension.
Received: April 30, 1997 相似文献
10.
Paola Bandieri 《Annali dell'Universita di Ferrara》1989,35(1):163-175
Summary In this paper we prove that the minimum among all regular genera of the graphs representing a 3-manifold with boundaryM
3 can always be obtained by a crystallization. As a consequence, we also prove that every 3-coloured graph representing ∂M
3 is the boundary of a 4-coloured graph which representsM
3 and whose genus equals the regular genus ofM
3.
Work performed under the auspices of the G.N.S.A.G.A.-C.N.R., and within the Project ?Geometria delle varietà differenziabili?, supported by M.P.I. of Italy. 相似文献
Riassunto In questo lavoro si prova che ogni 3-varietà con bordoM 3 ammette sempre una cristallizzazione di genere minimo. Come conseguenza, si ottiene che ogni grafo 3-colorato che rappresenta ∂M 3 è il bordo di un grafo 4-colorato che rappresentaM 3, il cui genere è uguale al genere regolare diM 3.
Work performed under the auspices of the G.N.S.A.G.A.-C.N.R., and within the Project ?Geometria delle varietà differenziabili?, supported by M.P.I. of Italy. 相似文献
11.
M. Belliart 《Commentarii Mathematici Helvetici》2002,77(3):524-548
Let M be a closed connected real analytic manifold; let be a free group on two generators. The set of analytic actions of on M endowed with Taken‚s topology contains a nonempty open subset whose corresponding actions share three properties: (a) they
have every orbit dense, (b) they leave invariant no geometric structure on M, (c) any homeomorphism conjugating two of them is analytic.
Received: October 3, 2001 相似文献
12.
Katia Rosenvald Frensel 《Bulletin of the Brazilian Mathematical Society》1996,27(2):129-144
Letx:M
2N
3 be a stable immersion with constant mean curvatureH of a complete orientable surfaceM
2 into a complete oriented three dimensional Riemannian manifoldN
3. In this paper we prove that, ifM
2 is compact andH
2> –1/2 inf
M
Ricc
N
, thenM
2 has genusg3, here Ricc
N
is the Ricci curvature ofN
3. We also prove that, ifM
2 is complete non compact andN
2 has bounded geometry, the area ofM
2 is infinite in the metric induced byx. In this case, ifH
2–1/2 inf
M
Ricc
N
thenx is umbilic and the equality holds. 相似文献
13.
The sum of the total curvatures of two orientable orthogonal foliations on the unit sphereS
2⊂R
3 is at least 4Π. The total curvature of a foliation with saddle singularities on a closed hyperbolic surfaceM is at least (12 Log 2–6 Log 3) ... |χ(M)|.
相似文献
14.
Let M be a map on a surface F
2. A geometric realization of M is an embedding of F
2 into a Euclidian 3-space ℝ3 with no self-intersection such that each face of M is a flat polygon. In Bonnington and Nakamoto (Discrete Comput. Geom. 40:141–157, 2008), it has been proved that every triangulation G on the projective plane has a face f such that the triangulation G−f on the M?bius band obtained from G by removing the interior of f has a geometric realization. In this paper, we shall characterize such a face f of G. 相似文献
15.
Joe J. Perez 《Journal of Geometric Analysis》2009,19(1):87-106
Let G be a unimodular Lie group, X a compact manifold with boundary, and M be the total space of a principal bundle G→M→X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if G acts by holomorphic transformations in M, then the Laplacian
on M has the following properties: The kernel of □ restricted to the forms Λ
p,q
with q>0 is a closed, G-invariant subspace in L
2(M,Λ
p,q
) of finite G-dimension. Secondly, we show that if q>0, then the image of □ contains a closed, G-invariant subspace of finite G-codimension in L
2(M,Λ
p,q
). These two properties taken together amount to saying that □ is a G-Fredholm operator. It is a corollary of the first property mentioned that the reduced L
2-Dolbeault cohomology spaces
of M are finite G-dimensional for q>0. The boundary Laplacian □
b
has similar properties.
相似文献
16.
Alla Sargsyan 《Arkiv f?r Matematik》2012,50(1):183-197
Let M be a smooth hypersurface of constant signature in CP
n
, n≥3. We prove the regularity for on M in bidegree (0,1). As a consequence, we show that there exists no smooth hypersurface in CP
n
, n≥3, whose Levi form has at least two zero-eigenvalues. 相似文献
17.
Let Mn be a closed Riemannian manifold with a nontrivial second homology group. In this paper we prove that there exists a geodesic net on Mn of length at most 3 diameter(Mn). Moreover, this geodesic net is either a closed geodesic, consists of two geodesic loops emanating from the same point, or consists of three geodesic segments between the same endpoints. Geodesic nets can be viewed as the critical points of the length functional on the space of graphs immersed into a Riemannian manifold. One can also consider other natural functionals on the same space, in particular, the maximal length of an edge. We prove that either there exists a closed geodesic of length ≤ 2 diameter(Mn), or there exists a critical point of this functional on the space of immersed θ-graphs such that the value of the functional does not exceed the diameter of Mn. If n=2, then this critical θ-graph is not only immersed but embedded.Mathematics Subject Classifications (2000). 53C23, 49Q10 相似文献
18.
John Hempel 《Inventiones Mathematicae》1982,67(1):133-142
LetMS
3,P
3 be a closed, orientable irreducible 3-manifold which admits an orientation reversing involution :MM. If dim(Fix )=0, suppose 1 (M) has a subgroup of even index. We show thatM has finite coverMMM} with 1(M<0). As an application we show that the hyperbolic dodecahedral space has a finite cover with positive 1st betti number. 相似文献
19.
We compute for all orientable irreducible geometric 3-manifolds certain complexity functions that approximate from above Matveev's
natural complexity, known to be equal to the minimal number of tetrahedra in a triangulation. We can show that the upper bounds
on Matveev's complexity implied by our computations are sharp for thousands of manifolds, and we conjecture they are for infinitely
many, including all Seifert manifolds. Our computations and estimates apply to all the Dehn fillings of M
6
1
3
(the complement of the three-component chain-link, conjectured to be the smallest triply cusped hyperbolic manifold), whence
to infinitely many among the smallest closed hyperbolic manifolds. Our computations are based on the machinery of the decomposition
into ‘bricks’ of irreducible manifolds, developed in a previous paper. As an application of our results we completely describe
the geometry of all 3-manifolds of complexity up to 9. 相似文献
20.
Sóstenes L. Lins 《Aequationes Mathematicae》1995,49(1):214-233
Summary A colored triangulation of a 3-manifoldM
3 is a decomposition into tetrahedra so that each vertex of them receive one of the colors 0, 1, 2, 3 in such a way that each tetrahedron has four differently colored vertices. From the combinatorics of the dual of a colored triangulation forM
3 we provide an easy algorithm to get a special kind of intersection matrix; from this matrix and from the torsion coefficients of the firstZ-homology group ofM
3 we provide a formula which yields its linking numbers. 相似文献