Coamenable normal subgroups of Borel-Anosov subgroups preserve the Riemannian critical exponent but not the full limit cone or growth indicator; rigidity holds exactly on the opposition-invariant directions, and counterexamples show this is sharp.
Confined subgroups in groups with contracting elements
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Directional growth of coamenable normal subgroups: counterexamples and rigidity
Coamenable normal subgroups of Borel-Anosov subgroups preserve the Riemannian critical exponent but not the full limit cone or growth indicator; rigidity holds exactly on the opposition-invariant directions, and counterexamples show this is sharp.