Related papers: Polar actions on complex hyperbolic spaces

We give solutions to several decision problems in word hyperbolic groups

We give a sufficient condition for isometric actions to have the congruency of orbits, that is, all orbits are isometrically congruent to each other. As applications, we give simple and unified proofs for some known congruence results, and…

The aim of this paper is to classify the cohomogeneity one conformal actions on the three-dimensional essential Riemannian spaces, up to orbit equivalence. Among other results, the representations of all connected Lie groups acting with…

We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.

In this paper, we classify the groups of semisimilarities of finite classical polar spaces with exactly two orbits on the singular or isotropic points. As a byproduct, we obtain many highly symmetric regular sets in the point graphs of…

We show that the equivariant cohomology of any hyperpolar action of a compact and connected Lie group on a symmetric space of compact type is a Cohen-Macaulay ring. This generalizes some results previously obtained by the authors.

For a hypersurface defined by a complex analytic function, we obtain a chain complex of free abelian groups, with ranks given in terms of relative polar multiplicities, which has cohomology isomorphic to the reduced cohomology of the real…

We develop the foundations of the theory of relatively geometric actions of relatively hyperbolic groups on CAT(0) cube complexes, a notion introduced in our previous work [5]. In the relatively geometric setting we prove: full relatively…

We indicate a C-Fuchsian counter-example to the result with the above title announced at http://www.maths.dur.ac.uk/events/Meetings/LMS/2011/GAL11/program.pdf and prove a stronger statement.

We define a generalized Berezin transforms on line bundle over the complex hyperbolic space and we give it as a functions of the G-invariant laplacian on the line bundles.

We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.

Recently, Haase and Ilten initiated the study of classifying algebraically hyperbolic surfaces in toric threefolds. We complete this classification for $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$, $\mathbb{P}^2 \times…

Some classical polar spaces admit polar spaces of the same rank as embedded polar spaces (often arisen as the intersection of the polar space with a non-tangent hyperplane). In this article we look at sets of generators that behave…

This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' functions on a quantum hyperbolic space and on the associated…

We extend recent orbit counts for finitely generated semigroups acting on $\mathbb{P}^N$ to certain infinitely generated, polarized semigroups acting on projective varieties. We then apply these results to semigroup orbits generated by some…

We study isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on the Minkowski space whose orbit spaces are non-Hausdorff. We show that…

We consider various notions of equivalence in the space of bounded operators on a Hilbert space, in particular modulo finite rank, modulo Schatten $p$-class, and modulo compact. Using Hjorth's theory of turbulence, the latter two are shown…

In this article, we construct partial periodic quotients of groups which have a non-elementary acylindrical action on a hyperbolic space. In particular, we provide infinite quotients of mapping class groups where a fixed power of every…

We prove that for any countable group acting virtually specially on a CAT(0) cube complex, the orbit equivalence relation induced by its action on the Roller boundary is hyperfinite. This can be considered as a generalization of…

Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.