DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, April 28 Communications 326 3:45 pm

Rigidity of quasi-isometries for some hyperbolic buildings

Herve Pajot (Universit de Cergy, France)

In this talk, I would like to explain the main steps of the proof of this following result (joint work with Marc Bourdon).

Theorem: Let Δ be a Fuchsian building with right angles. Then, every quasi-isometry F : Δ → Δ is at bounded distance fron an isometry ϕ : Δ → Δ.

In particular, I will discuss the following points:

• Definition and basic properties of Fuchsian buildings and their boundaries.

• Conformal structure on the boundary of Fuchsian buildings (differentiability of quasiconformal mappings, Liouville type theorem, …).