In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the met...In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain condi- tions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B（n） = {g ∈ G／ │g│suЭe≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.展开更多
In this paper, a class of metric spaces which include Hilbert spaces and Hadamard manifolds are defined. And the expanders cannot be coarsely embedded into this class of metric spaces are proved.
In this note, we prove a concentration theorem of （R,p）-anders. As a simple corollary, one can prove that （X, p）-anders do not admit coarse embeddings into Hadamard manifolds with bounded sectional curvatures.
Let X and Y be two pointed metric spaces.In this article,we give a generalization of the Cheng-Dong-Zhang theorem for coarse Lipschitz embeddings as follows:If f:X→Y is a standard coarse Lipschitz embedding,then for ...Let X and Y be two pointed metric spaces.In this article,we give a generalization of the Cheng-Dong-Zhang theorem for coarse Lipschitz embeddings as follows:If f:X→Y is a standard coarse Lipschitz embedding,then for each x^(*)∈Lip_(0)(X)there existα,γ>0 depending only on f and Q_(x)*∈Lip_(0)(Y)with‖Q_(x)*‖_(Lip)≤α‖x^(*)‖_(Lip)such that|Q_(x)*f(x)-x^(*)(x)|≤γ‖x^(*)‖_(Lip),for all x∈X.Coarse stability for a pair of metric spaces is studied.This can be considered as a coarse version of Qian Problem.As an application,we give candidate negative answers to a 58-year old problem by Lindenstrauss asking whether every Banach space is a Lipschitz retract of its bidual.Indeed,we show that X is not a Lipschitz retract of its bidual if X is a universally left-coarsely stable space but not an absolute cardinality-Lipschitz retract.If there exists a universally right-coarsely stable Banach space with the RNP but not isomorphic to any Hilbert space,then the problem also has a negative answer for a separable space.展开更多
基金supported by the National Natural Science Foundation of China(No.11301566)the Postdoc Scholarship(No.2012M511900)
文摘In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain condi- tions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B（n） = {g ∈ G／ │g│suЭe≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.
文摘In this paper, a class of metric spaces which include Hilbert spaces and Hadamard manifolds are defined. And the expanders cannot be coarsely embedded into this class of metric spaces are proved.
文摘In this note, we prove a concentration theorem of （R,p）-anders. As a simple corollary, one can prove that （X, p）-anders do not admit coarse embeddings into Hadamard manifolds with bounded sectional curvatures.
基金Supported by National Natural Science Foundation of China(Grant Nos.12126329,12171266,12126346,12101234)Simons Foundation(Grant No.585081)+6 种基金Educational Commission of Fujian Province(Grant No.JAT190589)Natural Science Foundation of Fujian Province(Grant No.2021J05237)the research start-up fund of Jimei University(Grant No.ZQ2021017)the research start-up fund of Putian University(Grant No.2020002)the Natural Science Foundation of Hebei Province(Grant No.A2022502010)the Fundamental Research Funds for the Central Universities(Grant No.2023MS164)the Natural Science Foundation of Fujian Province(Grant No.2023J01805)。
文摘Let X and Y be two pointed metric spaces.In this article,we give a generalization of the Cheng-Dong-Zhang theorem for coarse Lipschitz embeddings as follows:If f:X→Y is a standard coarse Lipschitz embedding,then for each x^(*)∈Lip_(0)(X)there existα,γ>0 depending only on f and Q_(x)*∈Lip_(0)(Y)with‖Q_(x)*‖_(Lip)≤α‖x^(*)‖_(Lip)such that|Q_(x)*f(x)-x^(*)(x)|≤γ‖x^(*)‖_(Lip),for all x∈X.Coarse stability for a pair of metric spaces is studied.This can be considered as a coarse version of Qian Problem.As an application,we give candidate negative answers to a 58-year old problem by Lindenstrauss asking whether every Banach space is a Lipschitz retract of its bidual.Indeed,we show that X is not a Lipschitz retract of its bidual if X is a universally left-coarsely stable space but not an absolute cardinality-Lipschitz retract.If there exists a universally right-coarsely stable Banach space with the RNP but not isomorphic to any Hilbert space,then the problem also has a negative answer for a separable space.
