Related papers: Lazy orbits: an optimization problem on the sphere

Consider an orientable compact surface in three dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic…

The purpose of this note is to give a classification of the orbital structure of certain reductive group actions on the Lagrangian Grassmanian. The groups under consideration are $Sp \times Sp$ and $GL$. The classification of $Sp \times Sp$…

We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational…

In this paper we study the scalar geometries occurring in the dimensional reduction of minimal five-dimensional supergravity to three Euclidean dimensions, and find that these depend on whether one first reduces over space or over time. In…

Let $G$ be a closed permutation group on a countably infinite set $\Omega$, which acts transitively but not highly transitively. If $G$ is oligomorphic, has no algebraicity and weakly eliminates imaginaries, we prove that any probability…

Let $k$ be a field, let $G$ be a reductive algebraic group over $k$, and let $V$ be a linear representation of $G$. Geometric invariant theory involves the study of the $k$-algebra of $G$-invariant polynomials on $V$, and the relation…

We describe the invariant metrics on real flag manifolds and classify those with the following property: every geodesic is the orbit of a one-parameter subgroup. Such a metric is called g.o. (geodesic orbit). In contrast to the complex…

We discuss the classification problem for the unitary easy quantum groups, under strong axioms, of noncommutative geometric nature. Our main results concern the intermediate easy quantum groups $O_N\subset G\subset U_N^+$. To any such…

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies to its possible homomorphisms into other…

For each group $G$ having an infinite normal subgroup with the relative property (T) (for instance $G = H \times K$ where $H$ is infinite with property (T) and $K$ is arbitrary), and any countable abelian group $\Lambda$ we construct free…

Let $X$ be a Hadamard manifold, and $\Gamma$ a non-elementary discrete group of isometries of $X$ which contains a rank one isometry. We relate the ergodic theory of the geodesic flow of the quotient orbifold $M=X/\Gamma$ to the behavior of…

Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…

We obtain many results and solve some problems about feebly compact paratopological groups. We obtain necessary and sufficient conditions for such a group to be topological. One of them is the quasiregularity. We prove that each…

Let G be a reductive group over a commutative ring R. We say that G has isotropic rank >=n, if every normal semisimple reductive R-subgroup of G contains (G_m)^n. We prove that if G has isotropic rank >=1 and R is a regular domain…

Geodesic orbit spaces are those Riemannian homogeneous spaces (G/H,g) whose geodesics are orbits of one-parameter subgroups of G. We classify the simply connected geodesic orbit spaces where G is a compact Lie group of rank two. We prove…

Let $\mathbb{K}$ be an unramified quadratic extension of $\mathbb{Q}_{p}$ for a fixed $p>2$. Projective general linear groups $G=\operatorname{PGL}_{2}(\mathbb{K})$ and $H=\operatorname{PGL}_{2}(\mathbb{Q}_{p})$ act transitively on…

For each arbitrary finite group $G$, we consider a suitable notion of Gromov Hausdorff distance between compact $G$ metric spaces and derive lower bounds based on equivariant topology methods. As applications, we prove equivariant rigidity…

The local Euler obstructions and the Euler characteristics of linear sections with all hyperplanes on a stratified projective variety are key geometric invariants in the study of singularity theory. Despite their importance, in general it…

The hyperoctahedral group $H$ in $n$ dimensions (the Weyl group of Lie type $B_n$) is the subgroup of the orthogonal group generated by all transpositions of coordinates and reflections with respect to coordinate hyperplanes. A finite set…

The hyperbolic space $ \H^d$ can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of linear isometries of the Minkowski space such that $\H^d/\Gamma$ is a compact…