Second-order hyperbolic Fuchsian systems and applications

Stable and conservative time propagators for second order hyperbolic systems

In this paper we construct a hierarchy of arbitrary high (even) order accurate explicit time propagators for semi-discrete second order hyperbolic systems. An accurate semi-discrete problem is obtained by approximating the corresponding spatial derivatives using high order accurate finite difference operators satisfying the summation by parts rule. In order to obtain a strictly stable semi-disc...

Well-posed Quasi-linear Second-order Hyperbolic Systems with Applications to Nonlinear Elastodynamics and General Relativity

Noncompact Fuchsian and quasi-Fuchsian surfacesin hyperbolic 3--manifolds

Given a noncompact quasi-Fuchsian surface in a finite volume hyperbolic 3–manifold, we introduce a new invariant called the cusp thickness, that measures how far the surface is from being totally geodesic. We relate this new invariant to the width of a surface, which allows us to extend and generalize results known for totally geodesic surfaces. We also show that checkerboard surfaces provide e...

Quasilinear Symmetric Hyperbolic Fuchsian Systems in Several Space Dimensions

We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an extension of earlier work by the authors for the same problem in one space dimension.

Complex hyperbolic quasi-Fuchsian groups

A complex hyperbolic quasi-Fuchsian group is a discrete, faithful, type preserving and geometrically finite representation of a surface group as a subgroup of the group of holomorphic isometries of complex hyperbolic space. Such groups are direct complex hyperbolic generalisations of quasi-Fuchsian groups in three dimensional (real) hyperbolic geometry. In this article we present the current st...