arXiv subjects

Wenyuan Yang

Publications and source records attributed to Wenyuan Yang.

47 records · Page 3Linked to original sources

arXiv2020

Large quotients of group actions with a contracting element

For any proper action of a non-elementary group $G$ on a proper geodesic metric space, we show that if $G$ contains a contracting element, then there exists a sequence of proper quotient groups whose growth rate tends to the growth rate of $G$. Similar statements are obtained for a product of proper actions with contracting elements. The tools involved in this paper include the extension lemma for the construction of large tree, the theory of rotating families developed by F. Dahmani, V. Guirardel and D. Osin, and the construction of a quasi-tree of metric spaces introduced by M. Bestvina, K. Bromberg and K. Fujiwara. Several applications are given to CAT(0) groups and mapping class groups.

math.GR↗

arXiv2020

BDTF: A Blockchain-Based Data Trading Framework with Trusted Execution Environment

The need for data trading promotes the emergence of data market. However, in conventional data markets, both data buyers and data sellers have to use a centralized trading platform which might be dishonest. A dishonest centralized trading platform may steal and resell the data seller's data, or may refuse to send data after receiving payment from the data buyer. It seriously affects the fair data transaction and harm the interests of both parties to the transaction. To address this issue, we propose a novel blockchain-based data trading framework with Trusted Execution Environment (TEE) to provide a trusted decentralized platform for fair data trading. In our design, a blockchain network is proposed to realize the payments from data buyers to data sellers, and a trusted exchange is built by using a TEE for the first time to achieve fair data transmission. With these help, data buyers and data sellers can conduct transactions directly. We implement our proposed framework on Ethereum and Intel SGX, security analysis and experimental results have demonstrated that the framework proposed can effectively guarantee the fair completion of data tradings.

cs.CR↗

arXiv2020

Quasiconvexity in $3$-manifold groups

In this paper, we study strongly quasiconvex subgroups in a finitely generated $3$--manifold group $π_1(M)$. We prove that if $M$ is a compact, orientable $3$--manifold that does not have a summand supporting the Sol geometry in its sphere-disc decomposition then a finitely generated subgroup $H \le π_1(M)$ has finite height if and only if $H$ is strongly quasiconvex. On the other hand, if $M$ has a summand supporting the Sol geometry in its sphere-disc decomposition then $π_1(M)$ contains finitely generated, finite height subgroups which are not strongly quasiconvex. We also characterize strongly quasiconvex subgroups of graph manifold groups by using their finite height, their Morse elements, and their actions on the Bass-Serre tree of $π_1(M)$. This result strengthens analogous results in right-angled Artin groups and mapping class groups. Finally, we characterize hyperbolic strongly quasiconvex subgroups of a finitely generated $3$--manifold group $π_1(M)$ by using their undistortedness property and their Morse elements.

math.GR↗

arXiv2017

Martin boundary covers Floyd boundary

For finitely supported random walks on finitely generated groups $G$ we prove that the identity map on $G$ extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. This yields new results for relatively hyperbolic groups. Our key estimate relates the Green and Floyd metrics, generalizing results of Ancona for random walks on hyperbolic groups and of Karlsson for quasigeodesics. We then apply these techniques to obtain some results concerning the harmonic measure on the limit sets of geometrically finite isometry groups of Gromov hyperbolic spaces. .

math.GR↗

arXiv2017

Statistically convex-cocompact actions of groups with contracting elements

This paper presents a study of the asymptotic geometry of groups with contracting elements, with emphasis on a subclass of statistically convex-cocompact (SCC) actions. The class of SCC actions includes relatively hyperbolic groups, CAT(0) groups with rank-1 elements and mapping class groups, among others. We exploit an extension lemma to prove that a group with SCC actions contains large free sub-semigroups, has purely exponential growth and contains a class of barrier-free sets with a growth-tight property. Our study produces new results and recovers existing ones for many interesting groups through a unified and elementary approach.

math.GR↗

arXiv2017

Genericity of contracting elements in groups

In this paper, we establish that, for statistically convex-cocompact actions, contracting elements are exponentially generic in counting measure. Among others, the following exponential genericity results are obtained as corollaries for the set of hyperbolic elements in relatively hyperbolic groups, the set of rank-1 elements in CAT(0) groups, and the set of pseudo-Anosov elements in mapping class groups. Regarding a proper action, the set of non-contracting elements is proven to be growth-negligible. In particular, for mapping class groups, the set of pseudo-Anosov elements is generic in a sufficiently large subgroup, provided that the subgroup has purely exponential growth. By Roblin's work, we obtain that the set of hyperbolic elements is generic in any discrete group action on CAT(-1) space with finite BMS measure. Applications to the number of conjugacy classes of non-contracting elements are given for non-rank-1 geodesics in CAT(0) groups with rank-1 elements.

math.GR↗

arXiv2017

Purely exponential growth of cusp-uniform actions

Suppose that a countable group $G$ admits a cusp-uniform action on a hyperbolic space $(X,d)$ such that $G$ is of divergent type. The main result of the paper is characterizing the purely exponential growth type of the orbit growth function by a condition introduced by Dal'bo-Otal-Peigné. For geometrically finite Cartan-Hadamard manifolds with pinched negative curvature this condition ensures the finiteness of Bowen-Margulis-Sullivan measures. In this case, our result recovers a theorem of Roblin (in a weaker form). Our main tool is the Patterson-Sullivan measures on the Gromov boundary of $X$, and a variant of the Sullivan shadow lemma called partial shadow lemma. This allows us to prove that the purely exponential growth of either cones, or partial cones or horoballs is also equivalent to the condition of Dal'bo-Otal-Peigné. These results are further used in the paper \cite{YANG7}.

math.GR↗

arXiv2016

Patterson-Sullivan measures and growth of relatively hyperbolic groups

We prove that for a relatively hyperbolic group G there is a sequence of relatively hyperbolic proper quotients such that their growth rates converge to the growth rate of G. Under natural assumptions, the same conclusion holds for the critical exponent of a cusp-uniform action of G on a hyperbolic metric space. As a corollary, we obtain that the critical exponent of a torsion-free geometrically finite Kleinian group can be arbitrarily approximated by those of quotient groups. This resolves a question of Dal'bo-Peigné-Picaud-Sambusetti. Our approach is based on the study of Patterson-Sullivan measures on Bowditch boundary of a relatively hyperbolic group. The uniqueness and ergodicity of Patterson-Sullivan measures are proved when the group is divergent. We prove a variant of the Sullivan Shadow Lemma, called Partial Shadow Lemma. This tool allows us to prove several results on growth functions of balls and cones. One central result is the existence of a sequence of geodesic trees with growth rates sufficiently close to the growth rate of G, and transition points uniformly spaced in trees. By taking small cancellation over hyperbolic elements of high powers, we can embed these trees into properly constructed quotients of G. This proves the results in the previous paragraph.

math.GR↗

arXiv2014

Growth tightness for groups with contracting elements

We establish growth tightness for a class of groups acting geometrically on a geodesic metric space and containing a contracting element. As a consequence, any group with nontrivial Floyd boundary are proven to be growth tight with respect to word metrics. In particular, all non-elementary relatively hyperbolic group are growth tight. This generalizes previous works of Arzhantseva-Lysenok and Sambusetti. Another interesting consequence is that CAT(0) groups with rank-1 elements are growth tight with respect to CAT(0)-metric.

math.GR↗

arXiv2012

Combination of fully quasiconvex subgroups and its applications

In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the existence of closed surface subgroups in relatively hyperbolic groups.

math.GR↗

arXiv2011

Peripheral structures of relatively hyperbolic groups

In this paper, we introduce and characterize a class of parabolically extended structures for relatively hyperbolic groups. A characterization of relative quasiconvexity with respect to parabolically extended structures is obtained using dynamical methods. Some applications are discussed. The class of groups acting geometrically finitely on Floyd boundaries turns out to be easily understood. However, we also show that Dunwoody's inaccessible group does not act geometrically finitely on its Floyd boundary.

math.GR↗