共查询到19条相似文献,搜索用时 93 毫秒
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Xueping LI 《Frontiers of Mathematics in China》2019,14(2):349-380
We show that a closed piecewise fiat 2-dimensional Alexandrov space Σ can be bi-Lipschitz embedded into a Euclidean space such that the embedded image of Σ has a tubular neighborhood in a generalized sense. As an application, we show that for any metric space sufficiently close to Σ in the Gromov-Hausdorff topology, there is a Lipschitz Gromov-Hausdorff approximation. 相似文献
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利用量子对称群的概念,我们给出U_q(sl_n)-多项式、U_q(sl_n)-外积的定义,说明U_q(sl_n)的q-振子、q-旋量表示不过是U_q(sl_n)标准表示的量子对称、量子反称张量积,这和经典情形是一致的。 相似文献
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给出了Burago有界距离定理在非内蕴距离情形不成立的一个例子, 其论证基于R2中最优圆装填问题的经典答案. 相似文献
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设G为有限维半单李代数,参数q不是单位根.定义了一个具有弱Hopf代数结构的弱量子代数wU_q(■),构造了它的类群元素集,并给出了两个不同参数的弱量子代数同构的条件. 相似文献
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设(g)为有限维半单李代数,参数q不是单位根.定义了一个具有弱Hopf代数结构的弱量子代数wUq((g)),构造了它的类群元素集,并给出了两个不同参数的弱量子代数同构的条件. 相似文献
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Wei Wu 《Journal of Functional Analysis》2006,238(1):58-98
A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel's Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As applications, we show that a quantized metric space with 1-exact underlying matrix order unit space is a limit of matrix algebras with respect to quantized Gromov-Hausdorff distance, and that matrix algebras converge naturally to the sphere for quantized Gromov-Hausdorff distance. 相似文献
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Hanfeng Li 《Journal of Functional Analysis》2009,257(7):2325-2350
For a closed cocompact subgroup Γ of a locally compact group G, given a compact abelian subgroup K of G and a homomorphism satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations of the homogeneous space G/Γ, generalizing Rieffel's construction of quantum Heisenberg manifolds. We show that when G is a Lie group and G/Γ is connected, given any norm on the Lie algebra of G, the seminorm on induced by the derivation map of the canonical G-action defines a compact quantum metric. Furthermore, it is shown that this compact quantum metric space depends on ρ continuously, with respect to quantum Gromov-Hausdorff distances. 相似文献
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Joël Rouyer 《Topology and its Applications》2011,158(16):2140-2147
We prove that there is a residual subset of the Gromov-Hausdorff space (i.e. the space of all compact metric spaces up to isometry endowed with the Gromov-Hausdorff distance) whose elements enjoy several unexpected properties. In particular, they have zero lower box dimension and infinite upper box dimension. 相似文献
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C. Villani 《Journal of Functional Analysis》2008,255(9):2683-2708
A certain curvature condition, introduced by Ma, Trudinger and Wang in relation with the regularity of optimal transport, is shown to be stable under Gromov-Hausdorff limits, even though the condition implicitly involves fourth order derivatives of the Riemannian metric. Two lines of reasoning are presented with slightly different assumptions, one purely geometric, and another one combining geometry and probability. Then a converse problem is studied: prove some partial regularity for the optimal transport on a perturbation of a Riemannian manifold satisfying a strong form of the Ma-Trudinger-Wang condition. 相似文献
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Li Guang Wang 《数学学报(英文版)》2016,32(10):1214-1220
In this short note,we consider the perturbation of compact quantum metric spaces.We first show that for two compact quantum metric spaces(A,P) and(B,Q) for which A and B are subspaces of an order-unit space C and P and Q are Lip-norms on A and B respectively,the quantum Gromov–Hausdorff distance between(A,P) and(B,Q) is small under certain conditions.Then some other perturbation results on compact quantum metric spaces derived from spectral triples are also given. 相似文献
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Hanfeng Li 《Journal of Functional Analysis》2009,256(10):3368-2350
We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA(G) of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic actions of G over a locally compact Hausdorff space T the map T→EA(G) sending each t in T to the isomorphism class of the fibre at t is continuous if and only if the function counting the multiplicity of γ in each fibre is continuous over T for every equivalence class γ of irreducible unitary representations of G. Generalizations for arbitrary compact quantum groups are also obtained. In the case G is a compact group, the restriction of this topology on the subset of isomorphism classes of ergodic actions of full multiplicity coincides with the topology coming from the work of Landstad and Wassermann. Podle? spheres are shown to be continuous in the natural parameter as ergodic actions of the quantum SU(2) group. We also introduce a notion of regularity for quantum metrics on G, and show how to construct a quantum metric from any ergodic action of G, starting from a regular quantum metric on G. Furthermore, we introduce a quantum Gromov-Hausdorff distance between ergodic actions of G when G is separable and show that it induces the above topology. 相似文献
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A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data 总被引:1,自引:0,他引:1
Point clouds are one of the most primitive and fundamental manifold
representations. Popular sources of point clouds are three-dimensional
shape acquisition devices such as laser range scanners. Another
important field where point clouds are found is in the representation
of high-dimensional manifolds by samples. With the increasing
popularity and very broad applications of this source
of data, it is natural and important to work directly with this
representation, without having to go through the intermediate and
sometimes impossible and distorting steps of surface reconstruction.
A geometric framework for comparing manifolds given by point clouds
is presented in this paper. The underlying theory is based on
Gromov-Hausdorff distances, leading to isometry invariant and
completely geometric comparisons. This theory is embedded in a
probabilistic setting as derived from random sampling of manifolds,
and then combined with results on matrices of pairwise geodesic distances
to lead to a computational implementation of the framework. The theoretical and
computational results presented here are complemented with
experiments for real three-dimensional shapes. 相似文献
18.
Christina Sormani 《Advances in Mathematics》2007,213(1):405-439
The author defines and analyzes the 1/k length spectra, L1/k(M), whose union, over all k∈N is the classical length spectrum. These new length spectra are shown to converge in the sense that limk→∞K1/k(Mi)⊂L1/k(M)∪{0} as Mi→M in the Gromov-Hausdorff sense. Energy methods are introduced to estimate the shortest element of L1/k, as well as a concept called the minimizing index which may be used to estimate the length of the shortest closed geodesic of a simply connected manifold in any dimension. A number of gap theorems are proven, including one for manifolds, Mn, with Ricci?(n−1) and volume close to Vol(Sn). Many results in this paper hold on compact length spaces in addition to Riemannian manifolds. 相似文献
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Yuguang ZHANG 《数学年刊B辑(英文版)》2007,28(4)
Compact K(a)hler manifolds with semi-positive Ricci curvature have been investigated by various authors. From Peternell's work, if M is a compact K(a)hler n-manifold with semi-positive Ricci curvature and finite fundamental group, then the universal cover has a decomposition (M) ≌ X1 × … × Xm, where Xj is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xj satisfies Ho(Xj,Ωp) = 0. The purpose of this paper is to generalize this theorem to almost non-negative Ricci curvature K(a)hler manifolds by using the Gromov-Hausdorff convergence. Let M be a compact complex n-manifold with non-vanishing Euler number. If for any ε > 0, there exists a K(a)hler structure (Je,ge) on M such that the volume Volge(M) < V, the sectional curvature |K(gε)| < Λ2, and the Ricci-tensor Ric(gε)> -εgε, where ∨ and Λ are two constants independent of ε. Then the fundamental group of M is finite, and M is diffeomorphic to a complex manifold X such that the universal covering of X has a decomposition, (X) ≌ X1 × … × Xs, where Xi is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xi satisfies Ho(Xi, Ωp) = {0}, p > 0. 相似文献