14 citations · 32 across the 14 of their papers we have counts for
15 papers
Bending, entropy and proper affine actions of surface groups
Martin Bridgeman, Richard Canary, Andres Sambarino
We show that for any closed surface there is an explict neighborhood of the fuchsian locus in quasifuchsian space such that for every representation $ρ\in…
Schwarzian Bounds on Bending in Hyperbolic 3-Manifolds
Martin Bridgeman, Ming Hong Tee
The Schwarzian derivative provides a classical analytic measure of how far a holomorphic map of the disk is from being Möbius, with Nehari's bounds giving sharp criteria for unival…
Epstein Surfaces, -Volume, and the Osgood-Stowe Differential
Martin Bridgeman, Kenneth Bromberg
In a seminal paper, Epstein introduced the theory of what are now called Epstein surfaces, which construct surfaces in associated to a conformal metric on a domain i…
Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds
Martin Bridgeman, Kenneth Bromberg
We bound the derivative of complex length of a geodesic under variation of the projective structure on a closed surface in terms of the norm of the Schwarzian in a neighborhood of…
Universal Liouville action as a renormalized volume and its gradient flow
Martin Bridgeman, Kenneth Bromberg, Franco Vargas Pallete +1
The universal Liouville action (also known as the Loewner energy for Jordan curves) is a Kähler potential on the Weil-Petersson universal Teichmüller space, which is identified wit…
A bound on the -norm of a projective structure by the length of the bending lamination
Martin Bridgeman, Kenneth Bromberg
One can associate to a complex projective structure on a surface holomorphic quadratic differential via the Schwarzian derivative and a bending lamination via the Thurston…
-bounds for drilling short geodesics in convex co-compact hyperbolic 3-manifolds
Martin Bridgeman, Kenneth Bromberg
We give -bounds on the change in the complex projective structure on the boundary of conformally compact hyperbolic 3-manifold with incompressible boundary after drilling shor…
Convergence of the gradient flow of renormalized volume to convex cores with totally geodesic boundary
Martin Bridgeman, Kenneth Bromberg, Franco Vargas Pallete
We consider the Weil-Petersson gradient vector field of renormalized volume on the deformation space of convex cocompact hyperbolic structures on (relatively) acylindrical manifold…
Hessian of Hausdorff dimension on purely imaginary directions
Martin Bridgeman, Beatrice Pozzetti, Andrés Sambarino +1
We extend classical results of Bridgeman-Taylor and McMullen on the Hessian of the Hausdorff dimension on quasi-Fuchsian space to the class of (1,1,2)-hyperconvex representations,…
Strata Separation for the Weil-Petersson Completion and Gradient Estimates for Length Functions
Martin Bridgeman, Kenneth Bromberg
In general, it is difficult to measure distances in the Weil-Petersson metric on Teichmüller space. Here we consider the distance between strata in the Weil-Petersson completion of…
The Weil-Petersson gradient flow of renormalized volume and 3-dimensional convex cores
Martin Bridgeman, Jeffrey Brock, Kenneth Bromberg
In this paper, we use the Weil-Petersson gradient flow for renormalized volume to study the space of convex cocompact hyperbolic structures on the relatively acylindric…
Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures
Martin Bridgeman, Yunhui Wu
In this article we show that for every finite area hyperbolic surface of type and any harmonic Beltrami differential on , then the magnitude of at any point…
Schwarzian derivatives, projective structures, and the Weil-Petersson gradient flow for renormalized volume
Martin Bridgeman, Jeffrey Brock, Kenneth Bromberg
To a complex projective structure on a surface, Thurston associates a locally convex pleated surface. We derive bounds on the geometry of both in terms of the norms $\|ϕ_Σ\|_\i…
Bounds on Volume Increase under Dehn Drilling Operations
Martin Bridgeman
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…
The Structure and Enumeration of Link Projections
Martin Bridgeman
We define a decomposition of link projections whose pieces we call atoroidal graphs. We describe a surgery operation on these graphs and show that all atoroidal graphs can be gener…