Related papers: Mass in the Hyperbolic Plane

We discuss basic properties of several different width functions in the $n$-dimensional hyperbolic space such as continuity, and we also define a new hyperbolic width as the extension of Leichtweiss' width function. Then we prove a…

The motion of astronomical bodies and the centre of mass of the system is not always well perceived by students. One of the struggles is the conceptual change of reference frame, which is the same that held back the acceptance of the…

A basic point about hyperbolic groups is that they have "spaces at infinity" which are spaces of homogeneous type in the sense of Coifman and Weiss, and with a lot of self-similarity coming from the group. This short survey deals with some…

Localization and dilation procedures are discussed for infinite dimensional $\alpha$-concave measures on abstract locally convex spaces (following Borell's hierarchy of hyperbolic measures).

In this paper we improve the approach of a previous paper about the domino problem in the hyperbolic plane, see arXiv.cs.CG/0603093. This time, we prove that the general problem of the hyperbolic plane with \`a la Wang tiles is undecidable.

We try to understand how particles acquire mass in general, and in particular, how they acquire mass in the standard model and beyond.

This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.

The cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.

In the hyperbolic plane there are infinite regular lattices. From a fix vertex of a lattice tree graphs can be constructed recursively to the next layers with edges of the lattice. In this article we examine the properties of the growing of…

In this note, we study deformations of quaternionic hyperbolic lattices in larger quaternionic hyperbolic spaces and prove local rigidity results. On the other hand, surface groups are shown to be more flexible in quaternionic hyperbolic…

This article simply presents several coordinate systems for 2 and 3-dimensional hyperbolic spaces, describing the general solutions of Helmholtz equation in each one of these systems.

This short review surveys mass for two-dimensional asymptotically locally hyperbolic initial data sets. I explain the difficulties in defining mass in spatial dimension two, which are resolved via minimisation using a positive energy…

We consider closed curves in the hyperbolic space moving by the $L^2$-gradient flow of the elastic energy and prove well-posedness and long time existence. Under the additional penalisation of the length we show subconvergence to critical…

We obtain the coefficients of a new fundamental plane for supermassive black holes at the centers of elliptical galaxies, involving measured central black hole mass and photometric parameters which define the light distribution. The…

A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of…

We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in lines in the plane.

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives…

We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…

We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain…

It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this…