Martin Bridgeman

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Using the thermodynamics formalism, we introduce a notion of intersection for convex Anosov representations, show analyticity results for the intersection and the entropy, and rigidity results for the intersection. We use the renormalized intersection to produce a Out(Γ)-invariant Riemannian metric on the smooth points of the deformation space of convex,(More)
We studied 5 patients with immobilisation hypercalcemia. Plasma calcium was 3.28 +/- (SD) 0.26 mmol/l. Plasma parathyroid hormone (PTH) level was elevated in 3 patients and inappropriately detectable in 1. Nephrogenous cAMP, measured in 3 patients, was low-normal in 1 who had a normal PTH and zero in 2 who had elevated PTH. Quantitative bone histology was(More)
In this paper we investigate how the volume of hyperbolic manifolds increases under the process of removing a curve, that is, Dehn drilling. If the curve we remove is a geodesic we are able to show that for a certain family of manifolds the volume increase is bounded above by π · l where l is the length of the geodesic drilled. Also we construct examples to(More)
Using the thermodynamic formalism, we introduce a notion of intersection for projective Anosov representations, show analyticity results for the intersection and the entropy, and rigidity results for the intersection. We use the renormalized intersection to produce an Out(Γ)-invariant Riemannian metric on the smooth points of the deformation space of(More)
We show that any closed hyperbolic surface admitting a conformal automorphism with “many” fixed points is uniformly quasiconformally homogeneous, with constant uniformly bounded away from 1. In particular, there is a uniform lower bound on the quasiconformal homogeneity constant for all hyperelliptic surfaces. In addition, we introduce more restrictive(More)
We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain Ω ⊂ Ĉ to the boundary Dome(Ω) of the convex hull of its complement. As a corollary, one obtains explicit bounds on the quasi-isometry constant of the nearest point retraction with respect to the Poincaré metric when Ω is uniformly perfect.(More)
We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word hyperbolic group into a semi-simple Lie group. To each such representation we associate an Anosov flow encoding eigenvalue information, and the thermodynamic formalism gives us(More)