共查询到20条相似文献,搜索用时 906 毫秒
1.
Dan Knopf 《Journal of Geometric Analysis》2009,19(4):817-846
Valuable models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally $\mathcal{G}Valuable models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally
G\mathcal{G}
-invariant solutions on bundles
GN\hookrightarrowM \oversetp? Bn\mathcal{G}^{N}\hookrightarrow\mathcal{M}\,\overset{\pi }{\mathcal{\longrightarrow}}\,\mathcal{B}^{n}
, with
G\mathcal{G}
a nilpotent Lie group. In this paper, we establish convergence and asymptotic stability, modulo smooth finite-dimensional
center manifolds, of certain ℝ
N
-invariant model solutions. In case N+n=3, our results are relevant to work of Lott classifying the asymptotic behavior of all 3-dimensional Ricci flow solutions
whose sectional curvatures and diameters are respectively
O(t-1)\mathcal{O}(t^{-1})
and
O(t1/2)\mathcal{O}(t^{1/2})
as t→∞. 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.
Let M{\mathcal M} be a σ-finite von Neumann algebra and
\mathfrak A{\mathfrak A} a maximal subdiagonal algebra of M{\mathcal M} with respect to a faithful normal conditional expectation F{\Phi} . Based on Haagerup’s noncommutative L
p
space Lp(M){L^p(\mathcal M)} associated with M{\mathcal M} , we give a noncommutative version of H
p
space relative to
\mathfrak A{\mathfrak A} . If h
0 is the image of a faithful normal state j{\varphi} in L1(M){L^1(\mathcal M)} such that j°F = j{\varphi\circ \Phi=\varphi} , then it is shown that the closure of
{\mathfrak Ah0\frac1p}{\{\mathfrak Ah_0^{\frac1p}\}} in Lp(M){L^p(\mathcal M)} for 1 ≤ p < ∞ is independent of the choice of the state preserving F{\Phi} . Moreover, several characterizations for a subalgebra of the von Neumann algebra M{\mathcal M} to be a maximal subdiagonal algebra are given. 相似文献
4.
Bent and almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are studied in this paper. By calculating certain exponential sum and using a technique due to Hou (Finite Fields Appl 10:566–582,
2004), we obtain a degree bound for quasi-bent functions, and prove that almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are equivalent to a degenerate quadratic form. From the viewpoint of relative difference sets, we also characterize bent
functions on
\mathbbZp2{\mathbb{Z}_p^2} in two classes of M{\mathcal{M}} ’s and PS{\mathcal{PS}} ’s, and show that the graph set corresponding to a bent function on
\mathbbZp2{\mathbb{Z}_p^2} can be written as the sum of a graph set of M{\mathcal{M}} ’s type bent function and another group ring element. By using our characterization and some technique of permutation polynomial,
we obtain the result: a bent function must be of M{\mathcal{M}} ’s type if its corresponding set contains more than (p − 3)/2 flats. A problem proposed by Ma and Pott (J Algebra 175:505–525, 1995) is therefore partially answered. 相似文献
5.
Let
Md{\cal M}^d
be an arbitrary real normed space of finite dimension d ≥ 2. We define the metric capacity of
Md{\cal M}^d
as the maximal
m ? \Bbb Nm \in {\Bbb N}
such that every m-point metric space is isometric to some subset of
Md{\cal M}^d
(with metric induced by
Md{\cal M}^d
). We obtain that the metric capacity of
Md{\cal M}^d
lies in the range from 3 to
ë\frac32d
û+1\left\lfloor\frac{3}{2}d\right\rfloor+1
, where the lower bound is sharp for all d, and the upper bound is shown to be sharp for d ∈ {2, 3}. Thus, the unknown sharp upper bound is asymptotically linear, since it lies in the range from d + 2 to
ë\frac32d
û+1\left\lfloor\frac{3}{2}d\right\rfloor+1
. 相似文献
6.
Let ${\mathcal{M}_g}Let Mg{\mathcal{M}_g} denote the moduli space of compact Riemann surfaces of genus g and let Ag{\mathcal{A}_g} be the moduli space of principally polarized abelian varieties of dimension g. Let J : Mg ? Ag{J : \mathcal{M}_g \rightarrow \mathcal{A}_g} be the map which associates to a Riemann surface its Jacobian. The map J is injective, and the image Jg : = J(Mg){\mathcal{J}_g := J(\mathcal{M}_g)} is contained in a proper subvariety of Ag{\mathcal{A}_g} when g ≥ 4. The classical and long-studied Schottky problem is to characterize the Jacobian locus Jg{\mathcal{J}_g} in Ag{\mathcal{A}_g}. In this paper we address a large scale version of this problem posed by Farb and called the coarse Schottky problem: What does Jg{\mathcal{J}_g} look like “from far away”, or how “dense” is Jg{\mathcal{J}_g} in the sense of coarse geometry? The large scale geometry of Ag{\mathcal{A}_g} is encoded in its asymptotic cone, Cone¥(Ag){{\rm Cone}_\infty(\mathcal{A}_g)}, which is a Euclidean simplicial cone of real dimension g. Our main result asserts that the Jacobian locus Jg{\mathcal{J}_g} is “coarsely dense” in Ag{\mathcal{A}_g}, which implies that the subset of Cone¥(Ag){{\rm Cone}_\infty(\mathcal{A}_g)} determined by Jg{\mathcal{J}_g} actually coincides with this cone. The proof shows that the Jacobian locus of hyperelliptic curves is coarsely dense in Ag{\mathcal{A}_g} as well. We also study the boundary points of the Jacobian locus Jg{\mathcal{J}_g} in Ag{\mathcal{A}_g} and in the Baily–Borel and the Borel–Serre compactification. We show that for large genus g the set of boundary points of Jg{\mathcal{J}_g} in these compactifications is “small”. 相似文献
7.
We study the geometry of a tangent sphere bundle of a Riemannian manifold (M, g). Let M be an n-dimensional Riemannian manifold and T
r
M be the tangent bundle of M of constant radius r. The main theorem is that T
r
M equipped with the standard contact metric structure is η-Einstein if and only if M is a space of constant sectional curvature
\frac1r2{\frac{1}{r^2}} or
\fracn-2r2{\frac{n-2}{r^2}}. 相似文献
8.
Marcos M. Alexandrino 《Geometriae Dedicata》2010,149(1):397-416
Let F{\mathcal{F}} be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F{\mathcal{F}} we construct a regular Riemannian foliation [^(F)]{\hat{\mathcal{F}}} on a compact Riemannian manifold [^(M)]{\hat{M}} and a desingularization map [^(r)]:[^(M)]? M{\hat{\rho}:\hat{M}\rightarrow M} that projects leaves of [^(F)]{\hat{\mathcal{F}}} into leaves of F{\mathcal{F}}. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose
leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F{\mathcal{F}} are compact, then, for each small ${\epsilon >0 }${\epsilon >0 }, we can find [^(M)]{\hat{M}} and [^(F)]{\hat{\mathcal{F}}} so that the desingularization map induces an e{\epsilon}-isometry between M/F{M/\mathcal{F}} and [^(M)]/[^(F)]{\hat{M}/\hat{\mathcal{F}}}. This implies in particular that the space of leaves M/F{M/\mathcal{F}} is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {([^(M)]n/[^(F)]n)}{\{(\hat{M}_{n}/\hat{\mathcal{F}}_{n})\}}. 相似文献
9.
Ansten Mørch Klev 《Archive for Mathematical Logic》2009,48(7):691-703
Using infinite time Turing machines we define two successive extensions of Kleene’s O{\mathcal{O}} and characterize both their height and their complexity. Specifically, we first prove that the one extension—which we will
call O+{\mathcal{O}^{+}}—has height equal to the supremum of the writable ordinals, and that the other extension—which we will call O++{\mathcal{O}}^{++}—has height equal to the supremum of the eventually writable ordinals. Next we prove that O+{\mathcal{O}^+} is Turing computably isomorphic to the halting problem of infinite time Turing computability, and that O++{\mathcal{O}^{++}} is Turing computably isomorphic to the halting problem of eventual computability. 相似文献
10.
In this paper, we consider massless Dirac fields propagating in the outer region of de Sitter–Reissner–Nordstr?m black holes.
We show that the metric of such black holes is uniquely determined by the partial knowledge of the corresponding scattering
matrix S(λ) at a fixed energy λ ≠ 0. More precisely, we consider the partial wave scattering matrices S(λ, n) (here λ ≠ 0 is the fixed energy and
n ? \mathbbN*{n \in \mathbb{N}^{*}} denotes the angular momentum) defined as the restrictions of the full scattering matrix on a well chosen basis of spin-weighted
spherical harmonics. We prove that the mass M, the square of the charge Q
2 and the cosmological constant Λ of a dS-RN black hole (and thus its metric) can be uniquely determined from the knowledge
of either the transmission coefficients T(λ, n), or the reflexion coefficients R(λ, n) (resp. L(λ, n)), for all n ? L{n \in {\mathcal{L}}} where L{\mathcal{L}} is a subset of
\mathbbN*{\mathbb{N}^{*}} that satisfies the Müntz condition
?n ? L\frac1n = +¥{\sum_{n \in{\mathcal{L}}}\frac{1}{n} = +\infty} . Our main tool consists in complexifying the angular momentum n and in studying the analytic properties of the “unphysical” scattering matrix S(λ, z) in the complex variable z. We show, in particular, that the quantities
\frac1T(l,z){\frac{1}{T(\lambda,z)}},
\fracR(l,z)T(l,z){\frac{R(\lambda,z)}{T(\lambda,z)}} and
\fracL(l,z)T(l,z){\frac{L(\lambda,z)}{T(\lambda,z)}} belong to the Nevanlinna class in the region ${\{z \in \mathbb{C}, Re(z) > 0 \}}${\{z \in \mathbb{C}, Re(z) > 0 \}} for which we have analytic uniqueness theorems at our disposal. Eventually, as a by-product of our method, we obtain reconstruction
formulae for the surface gravities of the event and cosmological horizons of the black hole which have an important physical
meaning in the Hawking effect. 相似文献
11.
Sorin G. Gal 《Complex Analysis and Operator Theory》2012,6(2):515-527
Attaching to a compact disk
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} in the quaternion field
\mathbbH{\mathbb{H}} and to some analytic function in Weierstrass sense on
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} the so-called q-Bernstein operators with q ≥ 1, Voronovskaja-type results with quantitative upper estimates are proved. As applications, the exact orders of approximation
in
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} for these operators, namely
\frac1n{\frac{1}{n}} if q = 1 and
\frac1qn{\frac{1}{q^{n}}} if q > 1, are obtained. The results extend those in the case of approximation of analytic functions of a complex variable in disks
by q-Bernstein operators of complex variable in Gal (Mediterr J Math 5(3):253–272, 2008) and complete the upper estimates obtained for q-Bernstein operators of quaternionic variable in Gal (Approximation by Complex Bernstein and Convolution-Type Operators, 2009; Adv Appl Clifford Alg, doi:, 2011). 相似文献
12.
We study hypersurfaces in the Lorentz-Minkowski space
\mathbbLn+1{\mathbb{L}^{n+1}} whose position vector ψ satisfies the condition L
k
ψ = Aψ + b, where L
k
is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed k = 0, . . . , n − 1,
A ? \mathbbR(n+1)×(n+1){A\in\mathbb{R}^{(n+1)\times(n+1)}} is a constant matrix and
b ? \mathbbLn+1{b\in\mathbb{L}^{n+1}} is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature, open pieces of totally umbilical hypersurfaces
\mathbbSn1(r){\mathbb{S}^n_1(r)} or
\mathbbHn(-r){\mathbb{H}^n(-r)}, and open pieces of generalized cylinders
\mathbbSm1(r)×\mathbbRn-m{\mathbb{S}^m_1(r)\times\mathbb{R}^{n-m}},
\mathbbHm(-r)×\mathbbRn-m{\mathbb{H}^m(-r)\times\mathbb{R}^{n-m}}, with k + 1 ≤ m ≤ n − 1, or
\mathbbLm×\mathbbSn-m(r){\mathbb{L}^m\times\mathbb{S}^{n-m}(r)}, with k + 1 ≤ n − m ≤ n − 1. This completely extends to the Lorentz-Minkowski space a previous classification for hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}} given by Alías and Gürbüz (Geom. Dedicata 121:113–127, 2006). 相似文献
13.
We propose an algorithm to sample and mesh a k-submanifold M{\mathcal{M}} of positive reach embedded in
\mathbbRd{\mathbb{R}^{d}} . The algorithm first constructs a crude sample of M{\mathcal{M}} . It then refines the sample according to a prescribed parameter e{\varepsilon} , and builds a mesh that approximates M{\mathcal{M}} . Differently from most algorithms that have been developed for meshing surfaces of
\mathbbR 3{\mathbb{R} ^3} , the refinement phase does not rely on a subdivision of
\mathbbR d{\mathbb{R} ^d} (such as a grid or a triangulation of the sample points) since the size of such scaffoldings depends exponentially on the
ambient dimension d. Instead, we only compute local stars consisting of k-dimensional simplices around each sample point. By refining the sample, we can ensure that all stars become coherent leading
to a k-dimensional triangulated manifold [^(M)]{\hat{\mathcal{M}}} . The algorithm uses only simple numerical operations. We show that the size of the sample is O(e-k){O(\varepsilon ^{-k})} and that [^(M)]{\hat{\mathcal{M}}} is a good triangulation of M{\mathcal{M}} . More specifically, we show that M{\mathcal{M}} and [^(M)]{\hat{\mathcal{M}}} are isotopic, that their Hausdorff distance is O(e2){O(\varepsilon ^{2})} and that the maximum angle between their tangent bundles is O(e){O(\varepsilon )} . The asymptotic complexity of the algorithm is T(e) = O(e-k2-k){T(\varepsilon) = O(\varepsilon ^{-k^2-k})} (for fixed M, d{\mathcal{M}, d} and k). 相似文献
14.
Hiroaki Minami 《Archive for Mathematical Logic》2010,49(4):501-518
We investigate splitting number and reaping number for the structure (ω)
ω
of infinite partitions of ω. We prove that
\mathfrakrd £ non(M),non(N),\mathfrakd{\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}} and
\mathfraksd 3 \mathfrakb{\mathfrak{s}_{d}\geq\mathfrak{b}} . We also show the consistency results ${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and ${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})} . To prove the consistency
\mathfrakrd < add(M){\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and
\mathfraksd < cof(M){\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})} we introduce new cardinal invariants
\mathfrakrpair{\mathfrak{r}_{pair}} and
\mathfrakspair{\mathfrak{s}_{pair}} . We also study the relation between
\mathfrakrpair, \mathfrakspair{\mathfrak{r}_{pair}, \mathfrak{s}_{pair}} and other cardinal invariants. We show that
cov(M),cov(N) £ \mathfrakrpair £ \mathfraksd,\mathfrakr{\mathsf{cov}(\mathcal{M}),\mathsf{cov}(\mathcal{N})\leq\mathfrak{r}_{pair}\leq\mathfrak{s}_{d},\mathfrak{r}} and
\mathfraks £ \mathfrakspair £ non(M),non(N){\mathfrak{s}\leq\mathfrak{s}_{pair}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N})} . 相似文献
15.
Let M{\mathcal {M}} be a dense o-minimal structure, N{\mathcal {N}} an unstable structure interpretable in M{\mathcal {M}}. Then there exists X, definable in Neq{\mathcal {N}^{eq}}, such that X, with the induced N{\mathcal {N}}-structure, is linearly ordered and o-minimal with respect to that ordering. As a consequence we obtain a classification,
along the lines of Zilber’s trichotomy, of unstable t-minimal types in structures interpretable in o-minimal theories. 相似文献
16.
In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show
that the Whitehead manifold lacks such a metric, and in fact that
\mathbbR3{\mathbb{R}^3} is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible
noncompact manifolds of higher dimension exhibiting this curvature phenomenon. Lastly we characterize all connected oriented
3-manifolds with finitely generated fundamental group allowing such a metric. 相似文献
17.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
18.
David G. Ebin 《Geometric And Functional Analysis》2012,22(1):202-212
Let M be a compact manifold with a symplectic form ω and consider the group Dw{\mathcal{D}_\omega} consisting of diffeomorphisms that preserve ω. We introduce a Riemannian metric on M which is compatible with ω and use it to define an L
2-inner product on vector fields on M. Extending by right invariance we get a weak Riemannian metric on Dw{\mathcal{D}_\omega} . We show that this metric has geodesics which come from integral curves of a smooth vector field on the tangent bundle of
Dw{\mathcal{D}_\omega} . Then, estimating the growth of such geodesics, we show that they extend globally. 相似文献
19.
We study convergence of approximate identities on some complete semi-normed or normed spaces of locally L
p
functions where translations are isometries, namely Marcinkiewicz spaces Mp{\mathcal{M}^{p}} and Stepanoff spaces Sp{\mathcal{S}^p}, 1 ≤ p < ∞, as well as others where translations are not isometric but bounded (the bounded p-mean spaces M
p
) or even unbounded (Mp0{M^{p}_{0}}). We construct a function f that belongs to these spaces and has the property that all approximate identities fe * f{\phi_\varepsilon * f} converge to f pointwise but they never converge in norm. 相似文献
20.
Fernando Schwartz 《Annales Henri Poincare》2011,12(1):67-76
We consider asymptotically flat Riemannian manifolds with non-negative scalar curvature that are conformal to
\mathbbRn\ W, n 3 3{\mathbb{R}^{n}{\setminus} \Omega, n\ge 3}, and so that their boundary is a minimal hypersurface. (Here,
W ì \mathbbRn{\Omega\subset \mathbb{R}^{n}} is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by
\frac12(V/bn)(n-2)/n{\frac{1}{2}\left(V/\beta_{n}\right)^{(n-2)/n}}, where V is the Euclidean volume of Ω and β
n
is the volume of the Euclidean unit n-ball. This gives a partial proof to a conjecture of Bray and Iga (Commun. Anal. Geom. 10:999–1016, 2002). Surprisingly, we do not require the boundary to be outermost. 相似文献