Related papers: Induced Hausdorff metrics on quotient spaces

Let $\varphi$ and $\varphi'$ be two homotopic actions of the topological group $G$ on the topological space $X$. To an object $A$ in the $G$-equivariant derived category $D_{\varphi}(X)$ of $X$ relative to the action $\varphi$ we associate…

Suppose M is a connected PL 2-manifold and X is a compact connected subpolyhedron of M (X \neq 1pt, a closed 2-manifold). Let E(X, M) denote the space of topological embeddings of X into M with the compact-open topology and let E(X, M)_0…

Let (G,+) be a compact, abelian, and metrizable topological group. In this group we take $g\in G$ such that the corresponding automorphism t_g is ergodic. The main result of this paper is a new ergodic theorem for functions in L^1(G,M),…

In this paper we define and study a notion of discrete homology theory for metric spaces. Instead of working with simplicial homology, our chain complexes are given by Lipschitz maps from an $n$-dimensional cube to a fixed metric space. We…

Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where…

Let $(M,g)$ be a Riemannian manifold with Riemannian distance $\mathsf{d}_g$, and $\mathcal{M}(M)$ be the space of all non-negative Borel measures on $M$, endowed with the Hellinger-Kantorovich distance $\mathsf{H\! K}_{\mathsf{d}_g}$…

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the…

We carry out analysis and geometry on a marked configuration space $\Omega_X^{R_+}$ over a Riemannian manifold $X$ with marks from the space $R_+$ as a natural generalization of the work {\bf [}{\it J. Func. Anal}. {\bf 154} (1998),…

We give lower bound estimates for the macroscopic scale of coarse differentiability of Lipschitz maps from a Carnot group with the Carnot-Carath\'{e}odory metric $(G,\dcc)$ to a few different classes of metric spaces. Using this result, we…

In this paper, we study the interaction between the geodesic orbit (g.o.~in short) property and certain flag curvature conditions. A Finsler manifold is called g.o.~if each constant speed geodesic is the orbit of a one-parameter subgroup.…

Let $(M,g)$ be a complete non-compact Riemannian manifold together with a function $e^h$, which weights the Hausdorff measures associated to the Riemannian metric. In this work we assume lower or upper radial bounds on some weighted or…

In this paper we introduce an intrinsic version of the classical induction of representations for a subgroup $H$ of a (finite) group $G$, called here {\em geometric induction}, which associates to any, not necessarily transitive, $G$-set…

Let $(\mathcal{M}, Q)$ be a dg manifold. The space of vector fields with shifted degrees $(\mathcal{X}(\mathcal{M})[-1], L_Q)$ is a Lie algebra object in the homology category $\mathrm{H}((C^{\infty}_{\mathcal{M}},Q)\mathrm{-}\mathbf{mod})$…

We carry out analysis and geometry on a marked configuration space $\Omega^M_X$ over a Riemannian manifold $X$ with marks from a space $M$. We suppose that $M$ is a homogeneous space $M$ of a Lie group $G$. As a transformation group $\frak…

We study the geometry of the space of measures of a compact ultrametric space X, endowed with the L^p Wasserstein distance from optimal transportation. We show that the power p of this distance makes this Wasserstein space affinely…

We describe the structure of $d$-dimensional homogeneous Lorentzian $G$-manifolds $M=G/H$ of a semisimple Lie group $G$. Due to a result by N. Kowalsky, it is sufficient to consider the case when the group $G$ acts properly, that is the…

In this paper, we study the right invariant metric $d_{H^{\infty}}$ on the analytic automorphism group $\rm{Aut}(\mathbb{D})$ of the unit open disk $\mathbb{D}$ induced by maximal modulus, that is, $d_{H^{\infty}}(\varphi,…

We find all intrinsic measures of $C^{1,1}$ smooth submanifolds in the Engel group, showing that they are equivalent to the corresponding $d$-dimensional spherical Hausdorff measure restricted to the submanifold. The integer $d$ is the…

In this paper, we consider a Finsler sphere $(M,F)=(S^n,F)$ with the dimension $n>1$ and the flag curvature $K\equiv 1$. The action of the connected isometry group $G=I_o(M,F)$ on $M$, together with the action of $T=S^1$ shifting the…

Swarm and constellation reconfiguration can be viewed as motion of an unordered point configuration in an ambient space. Here, we provide persistence-stable, symmetry-invariant geometric representations for comparing and monitoring…