8 papers
Limit cones of multi-Fuchsian representations
Jeffrey Danciger, François Guéritaud, Fanny Kassel
We study the set of normalized multi-lengths for representations of closed surface groups and free groups into whose projections to $\mathrm{PSL}_2\m…
Polyhedral realisations of finite arc complexes using strip deformations
François Guéritaud, Pallavi Panda
We study infinitesimal deformations of complete hyperbolic surfaces with boundary and with ideal vertices, possibly decorated with horoballs. ``Admissible'' deformations are the on…
Combination theorems in convex projective geometry
Jeffrey Danciger, François Guéritaud, Fanny Kassel
We prove a general combination theorem for discrete subgroups of preserving properly convex open subsets in the projective space $\mathbb{P}(\mathbb{R}…
Uniform Lipschitz extension in bounded curvature
François Guéritaud
We prove a uniform extension result for contracting maps defined on subsets of Hadamard manifolds subject to curvature bounds.
Proper affine actions for right-angled Coxeter groups
Jeffrey Danciger, François Guéritaud, Fanny Kassel
For any right-angled Coxeter group on generators, we construct proper actions of on by right and left multiplication, and on the Lie algebra $\mathf…
Strip maps of small surfaces are convex
François Guéritaud
The strip map is a natural map from the arc complex of a bordered hyperbolic surface to the vector space of infinitesimal deformations of . We prove that the image of the st…