相关论文: Some metric properties of automorphisms of groups
In this paper, we focus on some characterizations for curves in the Galilean and Pseudo-Galilean space.
In this paper, we investigate some characterizations of involute -- evolute curves in dual space. Then the relationships between dual frenet frame and darboux vectors of these curves are found.
The goal of this paper is to present a number of problems about automorphism groups of nonpositively curved polyhedral complexes and their lattices, meant to highlight possible directions for future research.
We introduce and investigate a natural family of metrics on connected components of a rack. The metrics are closely related to certain bi-invariant metrics on the group of inner automorphisms of the rack. We also introduce a bounded…
Let G be a finite group, and $g \geq 2$. We study the locus of genus g curves that admit a G-action of given type, and inclusions between such loci. We use this to study the locus of genus g curves with prescribed automorphism group G. We…
An irreducible, algebraic curve $\mathcal X_g$ of genus $g\geq 2$ defined over an algebraically closed field $k$ of characteristic $\mbox{char } \, k = p \geq 0$, has finite automorphism group $\mbox{Aut} (\mathcal X_g)$. In this paper we…
We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.
This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being…
Let $A_1,...,A_k$ be a system of free factors of $F_n$. The group of relative automorphisms $Aut(F_n;A_1,...,A_k)$ is the group given by the automorphisms of $F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The…
Principal component method is used to study galactic globular clusters in 7- and 8-axis space of structural parameters. It is shown that the manifold properties of clusters with this set of parameters is determined mainly by two independent…
Pedestrians are often encountered walking in the company of some social relations, rather than alone. The social groups thus formed, in variable proportions depending on the context, are not randomly organised but exhibit distinct features,…
We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their…
A subset of a group is characteristic if it is invariant under every automorphism of the group. We study word length in fundamental groups of closed hyperbolic surfaces with respect to characteristic generating sets consisting of a finite…
We explore the relationship between subgroups and the possible shifts of finite type (SFTs) that can be defined on the group. In particular, we investigate two group invariants, weak periodicity and strong periodicity, defined via symbolic…
A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques…
Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degrees and the Cremona degrees,…
This paper studies the magnitude homology of graphs focusing mainly on the relationship between its diagonality and the girth. Magnitude and magnitude homology are formulations of the Euler characteristic and the corresponding homology,…
The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II_1 factors. Here are some sample results: (1) an automorphism is approximately…