Lorentz dynamics on closed $3$-manifolds

Flat Lorentz 3 - manifolds and cocompact

Essential Closed Surfaces in Bounded 3-manifolds

A question dating back to Waldhausen [10] and discussed in various contexts by Thurston (see [9]) is the problem of the extent to which irreducible 3-manifolds with infinite fundamental group must contain surface groups. To state our results precisely, it is convenient to make the definition that a map i : S # M of a closed, orientable connected surface S is essential if it is injective at the ...

Simple Closed Geodesics in Hyperbolic 3-Manifolds

This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only example of a complete nonelementary orientable hyperbolic 3-manifold that does not contain a simple closed geodesic. We do not assume that the manifold is geometrically finite or that it has finitely generated fundament...

The Conjugate Linearized Ricci Flow on Closed 3–Manifolds

We characterize the conjugate linearized Ricci flow on closed three– manifolds of bounded geometry and discuss its properties. In particular, we express the evolution of the metric and of its Ricci tensor in terms of the backward heat kernel of the conjugate linearized Ricci flow. These results provide various conservation laws and monotonicity formulas for the linearized flow.

Flat Lorentz 3-manifolds and cocompact Fuchsian groups

Mess deduces this result as part of a general theory of domains of dependence in constant curvature Lorentzian 3-manifolds. We give an alternate proof, using an invariant introduced by Margulis [18, 19] and Teichmüller theory. We thank Scott Wolpert for helpful conversations concerning Teichmüller theory. We also wish to thank Paul Igodt and the Algebra Research Group at the Katholieke Universi...