14 citations · 32 across the 14 of their papers we have counts for
5 papers · 1 filter
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…
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…
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,…
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…