Gabriel Pallier

On the large-scale sublinear geometry of Heintze spaces

The Heintze spaces are the connected homogeneous spaces of negative curvature. They include the rank one symmetric spaces of non-compact type, but display more diversity. The method that has proved fruitful in the study of their large-scale geometry is to translate the problems into questions of quasiconformal geometry on their boundaries at infinity and treat them by analysis.
In this talk I will describe methods aiming at distinguish Heintze spaces up to sublinearly biLipschitz equivalence, a relation introduced by Yves Cornulier in his study of the large-scale geometry of Lie groups. I will give asymptotic invariants obtained through the boundary and yielding a classification in the three dimensional case, and describe ongoing work on the higher-dimensional case.