A curvature-free 𝐿𝑜𝑔(2𝑘-1) theorem

Proceedings of the American Mathematical Society

Abstract

This paper presents a curvature-free version of the Log ( 2 k − 1 ) \text {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.

Authors 2

1. Florent Balacheff

   Universitat Autònoma de Barcelona

   Affiliation as printed

   Departament de Matemàtiques, Universitat Autònoma de Barcelona, 8193 Bellaterra, Spain

2. Louis Merlin Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics, Rheinisch-Westfälische Technische Hochschule (RWTH), Aachen, Germany