A curvature-free Log(2k-1) theorem

Florent Balacheff, Louis Merlin

Research output: Contribution to journalArticleResearchpeer-review


This paper presents a curvature-free version of the Log(2k-1) Theorem of Anderson, Canary, Culler, and Shalen [J. Differential Geometry 44 (1996), pp. 738–782]. It generalizes a result by Hou [J. Differential Geometry 57 (2001), no. 1, pp. 173–193] and its proof is rather straightforward once we know the work by Lim [Trans. Amer. Math. Soc. 360 (2008), no. 10, pp. 5089–5100] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the Collar Lemma in all dimensions.

Original languageEnglish
Pages (from-to) 2429-2434
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number6
Early online dateMar 2023
Publication statusPublished - 1 Jun 2023


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