相关论文: Jorgensen's inequality for quternionic hyperbolic …

In the present paper, we deal with a quasilinear elliptic equation involving a critical Sobolev exponent on non-compact Randers spaces. Under very general assumptions on the perturbation, we prove the existence of a non-trivial solution.…

Sides and medians are both Jacobi coordinate magnitudes, moreover then equably entering the spherical coordinates on Kendall's shape sphere and the Hopf coordinates. This motivates treating medians on the same footing as sides in triangle…

We give explicit bijective correspondences between three families of objects: certain pairs of quaternions, which we regard as spinors; certain flags in (1+4)-dimensional Minkowski space; and horospheres in 4-dimensional hyperbolic space…

We review our recent theoretical results about inequivalence between passive gravitational mass and energy for a composite quantum body at a macroscopic level. In particular, we consider macroscopic ensembles of the simplest composite…

Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…

This paper is a more succinct version of the author's 1993 UCLA mathematics thesis. It proves that any group quasi-isometric to the product of the hyperbolic plane with the real line is a finite extension of a cocompact lattice in either…

A non-elementary M\"obius group generated by two-parabolics is determined up to conjugation by one complex parameter and the parameter space has been extensively studied. In this paper, we use the results of \cite{GW} to obtain an…

We construct `structure invariants' of a one-ended, finitely presented group that describe the way in which the factors of its JSJ decomposition over two-ended subgroups fit together. For groups satisfying two technical conditions, these…

We provide a simple, combinatorial criteria for a hierarchically hyperbolic space to be relatively hyperbolic by proving a new formulation of relative hyperbolicity in terms of hierarchy structures. In the case of clean hierarchically…

We prove a non-archimedean analogue of J{\o}rgensen's inequality, and use it to deduce several algebraic convergence results. As an application we show that every dense subgroup of $\mathrm{SL}(\mathbb{Q}_p)$ contains two elements which…

Let $M$ be a finite volume hyperbolic manifold, we show the equidistribution in $M$ of the equidistant hypersurfaces to a finite volume totally geodesic submanifold $C$. We prove a precise asymptotic on the number of geodesic arcs of…

We show the existence of group-theoretic sections of certain geometrically pro-nilpotent by abelian arithmetic fundamental groups of hyperbolic curves over p-adic local fields which are non-geometric, i.e., which do not arise from rational…

We describe the point and contact equivalence groupoids of an important class of two-dimensional quasilinear hyperbolic equations. In particular, we prove that this class is normalized in the usual sense with respect to point…

We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…

We study the set of homomorphisms from a fixed finitely generated group into a family of groups which are `uniformly acylindrically hyperbolic'. Our main results reduce this study to sets of homomorphisms which do not diverge in an…

The authors establish the necessary and sufficient conditions under which certain combinations of Gaussian hypergeometric function and elementary function are monotone in the parameter, which generalize the recent results of generalized…

Some integrals of matrix spaces over a quaternionic field have been calculated in this work. The associated volume of hyperbolic matrix spaces over a quaternionic field has also been calculated by making use of these integrals, and it is of…

We show that arithmetic subgroups of semisimple groups of relative Q-type A_n, B_n, C_n, D_n, E_6, or E_7 have an exponential lower bound to their isoperimetric inequality in the dimension that is 1 less than the real rank of the semisimple…

In this note we show the existence of the hyperbolical geometric quantum phase that is different from the ordinary trigonometric geometric quantum phase. Gravitomagnetic charge (dual mass) is the gravitational analogue of magnetic monopole…

The hyperbolic plane admits a quasi-isometric embedding into a hyperbolic group if and only if the group is not virtually free.