Related papers: Inhomogeneous isoparametric hypersurfaces in compl…

An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is…

We discuss asymptotically hyperbolic manifold with a noncompact boundary which is close to a horosphere in a certain sense. The model case is a horoball or the complement of a horoball in standard hyperbolic space. We show some geometric…

We study the existence of starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic space.

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.

We give a complete classification of isoparametric hypersurfaces in a product space $M^2_{\kappa_1}\times M^2_{\kappa_2}$ of $2$-dimensional space forms for $\kappa_i\in \{-1,0,1\}$ with $\kappa_1\neq \kappa_2$. In fact we prove that any…

We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.

We prove existence and uniqueness of an unstable manifold for a degenerate hyperbolic map of the plane arising in statistics.

We present an infinite dimensional Banach space in which the set of hyperbolic linear isomorphisms in that space is not dense (in the norm topology) in the set of linear isomorphisms.

Let $x: \mathbf{M} \rightarrow {\mathbb Q}^{n+1}_1$ be a regular space-like hypersurface in the conformal space ${\mathbb Q}^{n+1}_1$. We classify all those hypersurfaces with parallel Blaschke tensor in the conformal space up to the…

We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.

Hyperbolic propagation offers exciting opportunities in nanophotonics, from sub-diffraction imaging to enhanced local density of states. This transport regime is typically induced by strong modulation of conductivity, i.e., with alternating…

We give a classification of integral lattices with virtually abelian symmetry group. As a consequence, we complete the classification of K3 surfaces with virtually abelian automorphism group. In the appendix we formulate an algorithm for…

In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…

This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…

We prove the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line, and such that the preimage of the extended real line under the projection map is…

We show that globally and regularly hyperbolic future geodesically incomplete isotropic universes, except for the standard all-encompassing `big crunch', can accommodate singularities of only one kind, namely, those having a non-integrable…

We compute and analyse the moduli space of those real projective structures on a hyperbolic 3-orbifold that are modelled on a single ideal tetrahedron in projective space. Parameterisations are given in terms of classical invariants,…

We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…

In this article, we prove a geometric inequality for star-shaped and mean-convex hypersurfaces in hyperbolic space by inverse mean curvature flow. This inequality can be considered as a generalization of Willmore inequality for closed…