Volume growth of horospheres in diagonalizable Heintze groups

Résumé fourni par la source

We study the volume growth of horospheres in a Heintze group of the form R ___ A R d with A a diagonal derivation. We conclude that the isometry and quasi-isometry classes of horospheres (with their intrinsic geometry) coincide. Furthermore, if A is not a scalar multiple of the identity, then there are exactly two such classes, characterized by their volume growth, which we calculate explicitly.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.