Let S be a compact orientable surface and f be an element of the group Homeo_0(S) of homeomorphisms of S isotopic to the identity. Denote by f a lift of f to the universal cover S of S. In this article, the following result is proved: If there exists a fundamental domain D of the covering S → S such that lim n→+∞ 1 d_n log(d_n) = 0, where d_n is the diameter of f~n(D), then the homeomorphism f is a distortion element of the group Homeo_0(S).
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机译：令S为致密可定向表面，f为S同位素同种异形的Homeo_0（S）组的元素。用f对S的通用覆盖S的fa提升表示。在本文中，证明以下结果：如果存在覆盖S→S的基本域D，使得lim n→+∞1 / n d_n log（ d_n）= 0，其中d_n是f〜n（D）的直径，则同胚性f是Homeo_0（S）组的变形元素。
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