In diagonal Heintze groups with non-scalar A, horospheres split into exactly two isometry and quasi-isometry classes, with the non-Euclidean class having volume growth of order r^k, k=(λ1+...+λd)/λ1.
Isometric Riemannian manifolds at infinity
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Volume growth of horospheres in diagonalizable Heintze groups
In diagonal Heintze groups with non-scalar A, horospheres split into exactly two isometry and quasi-isometry classes, with the non-Euclidean class having volume growth of order r^k, k=(λ1+...+λd)/λ1.