2025/05/22 by Courtois, Gilles, Lessa, Pablo, Sequeira, Emiliano
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.16450
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.