Hyperideal circle patterns

A ``hyperideal circle pattern'' in $S^2$ is a finite family of oriented circles, similar to the ``usual'' circle patterns but such that the closed disks bounded by the circles do not cover the whole sphere. Hyperideal circle patterns are directly related to hyperideal hyperbolic polyhedra, and also to circle packings. To each hyperideal circle pattern, one can associate an incidence graph and a set of intersection angles. We characterize the possible incidence graphs and intersection angles of hyperideal circle patterns in the sphere, the torus, and in higher genus surfaces. It is a consequence of a more general result, describing the hyperideal circle patterns in the boundaries of geometrically finite hyperbolic 3-manifolds (for the corresponding \C P^1-structures). This more general statement is obtained as a consequence of a theorem of Otal \cite{otal,bonahon-otal} on the pleating laminations of the convex cores of geometrically finite hyperbolic manifolds.Comment: 11 pages, 2 figures. Updated versions will be posted on http://picard.ups-tlse.fr/~schlenker Revised version: some corrections, better proof, added reference

Non-rigidity of spherical inversive distance circle packings

We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.Comment: 6 pages, one pictur

AdS manifolds with particles and earthquakes on singular surfaces

We prove two related results. The first is an ``Earthquake Theorem'' for closed hyperbolic surfaces with cone singularities where the total angle is less than $\pi$: any two such metrics in are connected by a unique left earthquake. The second result is that the space of ``globally hyperbolic'' AdS manifolds with ``particles'' -- cone singularities (of given angle) along time-like lines -- is parametrized by the product of two copies of the Teichm\"uller space with some marked points (corresponding to the cone singularities). The two statements are proved together.Comment: 18 pages, several figures. v2: improved exposition, several correction

Quasi-Fuchsian manifolds with particles

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than $\pi$: any first-order deformation changes either one of those angles or the conformal structure at infinity, with marked points corresponding to the endpoints of the singular lines. Moreover, any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone-manifold structure.Comment: Now 48 pages, no figure. v2: new title, various corrections, results extended to include graph singularities ("interacting particles"). v3: various corrections/improvements, in particular thanks to comments by an anonymous refere

Wakefield Land Conservation Education & Outreach Project

The Town of Wakefield has experienced an unprecedented growth explosion in the past seven years. Pressures to use heretofore undeveloped land for the construction of residential housing has threatened the natural resources of this community. The projected growth rate has the potential to severely impact Wakefield’s natural resources. While the town has undertaken a comprehensive revision of zoning, site plan and subdivision regulations, it is important that voluntary land protection measures are advanced to secure permanent protection of valuable resources