Related papers: Horizontal loops in Engel space

We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…

A vector space G is introduced such that the Galilei transformations are considered linear mappings in this manifold. The covariant structure of the Galilei Group (Y. Takahashi, Fortschr. Phys. 36 (1988) 63; 36 (1988) 83) is derived and the…

We introduce the concept of timelike entanglement entropy of Hawking radiation as a novel probe of the black hole information paradox. By analytically continuing black hole spacetimes to Euclidean signature, we define timelike correlations…

We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called…

For embedded 2-spheres in a 4-manifold sharing the same embedded transverse sphere homotopy implies isotopy, provided the ambient 4-manifold has no $\BZ_2$-torsion in the fundamental group. This gives a generalization of the classical light…

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…

We prove that non-Hilbertian separable Orlicz sequence spaces are ergodic, i.e., the equivalence relation $\mathbb{E}_0$ Borel reduces to the isomorphism relation between subspaces of every such space. This is done by exhibiting…

We embed spherical Rindler space -- a geometry with a spherical hole in its center -- in asymptotically AdS spacetime and show that it carries a gravitational entropy proportional to the area of the hole. Spherical AdS-Rindler space is…

We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared…

We calculate the topological entanglement entropy in bilayer quantum Hall systems, dividing the set of quantum numbers into four parts. This topological entanglement entropy allows us to draw a phase diagram in the parameter space of layer…

We consider divergent orbits of the group of diagonal matrices in the space of lattices in Euclidean space. We define two natural numerical invariants of such orbits: The discriminant - an integer - and the type - an integer vector. We then…

It was proved by Dodos and Ferenczi that the classes of Banach spaces with a separable dual and of separable reflexive Banach spaces are strongly bounded. In this note, we provide an isometric version of this result.

It has been argued that the entropy which one is computing in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field and that the calculation performed is not…

A subset of a convex body $B$ containing the origin in a Euclidean space is {\it parkable in $B$} if it can be translated inside $B$ in such a manner that the translate the origin. We provide characterizations of ellipsoids and of centrally…

In this note we give a short proof to the rigidity of volume entropy. The result says that for a closed manifold with Ricci curvature bounded from below, if the universal cover has maximal volume entropy, then it is the space form. This…

The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…

Quantitative bounds for random embeddings of $\mathbb{R}^{k}$ into Lorentz sequence spaces are given, with improved dependence on $\varepsilon$.

We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of…

A rotational subset, relative to a continuous transformation $T: \mathbb{T} \to \mathbb{T}$ on the unit circle, is a closed, invariant subset of $\mathbb{T}$ that is minimal and on which $T$ respects the standard orientation of the unit…