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991.
André Neves 《Inventiones Mathematicae》2007,168(3):449-484
We study singularities of Lagrangian mean curvature flow in ℂ
n
when the initial condition is a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are
unavoidable. More precisely, we construct Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are Hamiltonian
isotopic to a plane that, nevertheless, develop finite time singularities under mean curvature flow.
We then prove two theorems regarding the tangent flow at a singularity when the initial condition is a zero-Maslov class Lagrangian.
The first one (Theorem A) states that that the rescaled flow at a singularity converges weakly to a finite union of area-minimizing
Lagrangian cones. The second theorem (Theorem B) states that, under the additional assumptions that the initial condition
is an almost-calibrated and rational Lagrangian, connected components of the rescaled flow converges to a single area-minimizing Lagrangian cone, as opposed to a possible non-area-minimizing union of area-minimizing Lagrangian cones.
The latter condition is dense for Lagrangians with finitely generated H
1(L,ℤ). 相似文献
992.
Pierre Jammes 《manuscripta mathematica》2007,123(1):15-23
Let M
n
be an n-dimensional compact manifold, with n ≥ 3. For any conformal class C of riemannian metrics on M, we set , where μ
p,k
(M,g) is the kth eigenvalue of the Hodge laplacian acting on coexact p-forms. We prove that . We also prove that if g is a smooth metric such that , and n = 0,2,3 mod 4, then there is a non-zero corresponding eigenform of degree with constant length. As a corollary, on a four-manifold with non vanishing Euler characteristic, there is no such smooth
extremal metric. 相似文献
993.
Jean Gillibert 《Mathematische Annalen》2007,338(2):475-495
The so-called class-invariant homomorphism ψ measures the Galois module structure of torsors—under a finite flat group scheme
G—which lie in the image of a coboundary map associated to an isogeny between (Néron models of) abelian varieties with kernel
G. When the varieties are elliptic curves with semi-stable reduction and the order of G is coprime to 6, it is known that the homomorphism ψ vanishes on torsion points. In this paper, using Weil restrictions of
elliptic curves, we give the construction, for any prime number p > 2, of an abelian variety A of dimension p endowed with an isogeny (with kernel μ
p
) whose coboundary map is surjective. In the case when A has rank zero and the p-part of the Picard group of the base is non-trivial, we obtain examples where ψ does not vanish on torsion points.
Résumé Le class-invariant homomorphism permet de mesurer la structure galoisienne des torseurs—sous un schéma en groupes fini et plat G—qui sont dans l’image du cobord associé à une isogénie, de noyau G, entre des (modèles de Néron de) variétés abéliennes. Quand les variétés sont des courbes elliptiques à réduction semi-stable et que l’ordre de G est premier à 6, on sait que cet homomorphisme s’annule sur les points de torsion. Dans cet article, en nous servant de restrictions de Weil de courbes elliptiques, nous construisons, pour tout nombre premier p > 2, une variété abélienne A de dimension p munie d’une isogénie (de noyau μ p ) dont le cobord est surjectif. Si A est de rang nul, et si la p-partie du groupe de Picard de la base est non triviale, nous obtenons ainsi un exemple où le class-invariant homomorphism ne s’annule pas sur les points de torsion.相似文献
994.
ZHU Sheng-jiang DING Huai-bo J.H.Hamilton A.V.Ramayya CHE Xing-lai J.K.Hwang Y.X.Luo J.O.Rasmussen K.Li WANG Jian-guo XU Qiang GU Long YANG Yun-yi S.Frauendorf V.Dimitrov 《原子核物理评论》2009,26(Z1)
The level structures of neutron-rich ~(105)Mo,~(106)Mo,~(108)Mo and 110Ru nuclei in A≈100 region have been carefully investigated by coincidence measurements of the prompt γ-rays populated in the spontaneous fission of ~(252)Cf with the Gammasphere detector array.In 105Mo,one-phonon K =9/2 and two-phonon K=13/2 γ-vibrational bands have been identified.In ~(108)Mo,one-phonon γ-vibrational band is expanded and two-phonon γ-vibrational band has been identified.Two similar sets of bands in ~(106)Mo and ~(110)Ru are observed to high spins,which have been proposed as the soft chiral γ-vibrational bands.The characteristics for these γ-vibrational bands and chiral doublet bands have been discussed. 相似文献
995.
Starting from the definitions and the properties of reinforced renewal processes and reinforced Markov renewal processes,
we characterize, via exchangeability and de Finetti’s representation theorem, a prior that consists of a family of Dirichlet
distributions on the space of Markov transition matrices and beta-Stacy processes on distribution functions. Then, we show
that this family is conjugate and give some estimate results.
相似文献
相似文献
996.
<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Betti numbers of one-relator groups
We determine the L
2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the
L
2-cohomology of left-orderable groups, and deduce the non-L
2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.
Warren Dicks was Funded by the DGI (Spain) through Project BFM2003-06613. 相似文献
997.
Alexander Moretó 《Algebras and Representation Theory》2007,10(4):333-338
Given a group G, Γ(G) is the graph whose vertices are the primes that divide the degree of some irreducible character and two vertices p and q are joined by an edge if pq divides the degree of some irreducible character of G. By a definition of Lewis, a graph Γ has bounded Fitting height if the Fitting height of any solvable group G with Γ(G)=Γ is bounded (in terms of Γ). In this note, we prove that there exists a universal constant C such that if Γ has bounded Fitting height and Γ(G)=Γ then h(G)≤C. This solves a problem raised by Lewis.
Research supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, the FEDER and
Programa Ramón y Cajal. 相似文献
998.
Pavel Exner Takashi Ichinose Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2007,57(1):67-81
We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator.
Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive
assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the
situation when the usual non-decay measurement is replaced by a particular generalized observables in the sense of Davies. 相似文献
999.
Harold Widom 《Integral Equations and Operator Theory》2007,57(1):133-151
The solution of a problem arising in integrable systems requires sharp asymptotics for the inverses and determinants of truncated
Wiener-Hopf operators, both in the regular case (where the non-truncated Wiener-Hopf operator is invertible) and in singular
cases. This paper treats two cases where the symbol of the Wiener-Hopf operator has Fisher-Hartwig singularities, one double
zero or two simple zeros. We find formulas for the inverse that hold uniformly throughout the underlying interval with very
small error, and formulas for the determinant with very small error. 相似文献
1000.
Mathias Schulze 《manuscripta mathematica》2007,123(4):373-379
From the degree zero part of the logarithmic vector fields along analgebraic hypersurface singularity we identify the maximal
multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that
all such maximal tori are conjugate and in one–to–one correspondence to maximal tori in the linear jet of the embedded automorphism
group. These results are motivated by Kyoji Saito’s characterization of quasihomogeneity for isolated hypersurface singularities
[Saito in Invent. Math. 14, 123–142 (1971)] and extend previous work with Granger and Schulze [Compos. Math. 142(3), 765–778 (2006), Theorem 5.4] and of Hauser and Müller [Nagoya Math. J. 113, 181–186 (1989), Theorem 4]. 相似文献