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arXiv · 2505.16450

Volume growth of horospheres in diagonalizable Heintze groups

Gilles Courtois·Pablo Lessa·Emiliano Sequeira
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Abstract

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.

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Gilles Courtois, Pablo Lessa, Emiliano Sequeira. 2025-05-22. Volume growth of horospheres in diagonalizable Heintze groups. https://arxiv.org/abs/2505.16450

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