

Geometrical finiteness in strictly convex projective geometry
De Pierre-Louis Blayac


Local minimization of fuzziness under high symmetry
De Franco Vargas Pallete


The shape of the limit cone for positive representations
De Jeffrey Danciger
De Alex Nolte
Apparaît dans la collection : 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics
We will present a pair of flexible and degenerate constructions of objects related to Thurston’s Lipschitz metric on Teichmüller space. In particular, we will explain how to construct sums of Fuchsian representations of surface groups whose limit cones are polyhedra and how to construct irregular geodesics for Thurston’s Lipschitz metric on Teichmüller space. Both constructions are “as degenerate as possible” in appropriate senses. We will emphasize the close relationship of these constructions with a counterintuitive theorem of Thurston on the generic simplicity and stability of solutions to a length-ratio optimization problem on hyperbolic surfaces.