Metric properties on Lie groups of polynomial volume growth |
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Authors: | Nourredine Bounechada |
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Institution: | Université Pierre et Marie Curie, Paris VI, UFR 920, 175, rue du Chevaleret, 75013 Paris, France |
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Abstract: | It is well known that we have an algebraic characterization of connected Lie groups of polynomial volume growth: a Lie group G has polynomial volume growth if and only if it is of type R. In this paper, we shall give a geometric characterization of connected Lie groups of polynomial volume growth in terms of the distance distortion of the subgroups. More precisely, we prove that a connected Lie group G has polynomial volume growth if and only if every closed subgroup has a polynomial distortion in G. |
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Keywords: | 22E25 51K05 |
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