The classification of Kleinian groups of Hausdorff dimensions at most one and Burnside's conjecture

arXiv2102.05992MaRDI QIDQ6360389

Yong Hou

Publication date: 11 February 2021

Abstract: In this paper we provide the complete classification of convex cocompact Kleinian group of Hausdorff dimensions less than $1.$ In particular, we prove that every convex cocompact Kleinian group of Hausdorff dimension $<1$ is a classical Schottky group. This upper bound is sharp. The result implies that the converse of Burside's conjecture cite{Burside} is true: All non-classical Schottky groups must have Hausdorff dimension $ge1$. The prove of the theorem relies on the result of Hou cite{Hou}.

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