Related papers: Compact Hyperbolic Manifolds as Internal Worlds
I give a brief informal introduction to the idea and tests of large extra dimensions, focusing on the case in which the space-time manifold has a direct product structure. I then describe some attractive implementations in which the…
We present a family of examples of two dimensional, hyperbolic complex manifolds whose envelopes of holomorphy are not hyperbolic.
We give examples of harmonic maps between negatively curved manifolds with special properties. These negatively curved manifolds do not have the homotopy type of a locally symmetric space.
The goal of this paper is to study the geometry of cusped complex hyperbolic manifolds through their compactifications. We characterize toroidal compactifications with non-nef canonical divisor. We derive effective very ampleness results…
This paper investigates the generalizations and applications of weakly $p$-K\"ahler hyperbolic manifolds.
We show that a partially hyperbolic system can have at most a finite number of compact center-stable submanifolds. We also give sufficient conditions for these submanifolds to exist and consider the question of whether they can intersect…
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…
We obtain some restrictions on the topology of infinite volume hyperbolic manifolds. In particular, for any n and any closed negatively curved manifold M of dimension greater than 2, only finitely many hyperbolic n-manifolds are total…
The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…
We classify minimal extrinsically homogeneous submanifolds of complex hyperbolic spaces.
We discuss several ways of packing a hyperbolic surface with circles (of either varying radii or all being congruent) or horocycles, and note down some observations related to their symmetries (or the absence thereof).
We construct compact hyperbolic 3-manifolds with totally geodesic boundary, such that the closed 3-pseudomanifolds obtained by coning off the boundary components are negatively curved and contain locally convex subspaces whose fundamental…
We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the $L^2$ harmonic spaces on the universal cover of these manifolds. Other results include a Hard…
Negatively-curved, maximally symmetric hyperbolic spaces enjoy a number of remarkable properties that can be traced back to Riemannian geometry, group theory and algebraic geometry. In this note we recall some such properties and find $H_n$…
This article explores some properties of universal covers of compact Kahler manifolds, under the assumption of Caratheodory measure hyperbolicity. In particular, by comparing invariant volume forms, an inequality is established between the…
The goal of this paper is to study the deformations of compact K\"ahler hyperbolic manifolds. We propose slightly modified versions of K\"ahler hyperbolicity as a tool to provide a first step towards investigating the deformation openness…
The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (1) the…
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…
Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only…