Abstract
We give a lower bound on the boundary injectivity radius of the Margulis tubes with smooth boundary constructed by Buser, Colbois, and Dodziuk. This estimate depends on the dimension and a curvature bound only.
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References
Abert, M., Bergeron, N., Biringer, I., Gelander, T.: Convergence of normalize Betti numbers in nonpositive curvature. arXiv:1811.02520v2 [math.GT]
Ballmann, W., Gromov, M., Schroeder, V.: Manifolds of Nonpositive Curvature. Progress in Mathematics, vol. 61. Birkhäuser Boston Inc., Boston (1985)
Buser, P., Colbois, B., Dodziuk, J.: Tubes and eigenvalues for negatively curves manifolds. J. Geom. Anal. 3(1), 1–26 (1993)
Di Cerbo, L.F., Stern, M.: Harmonic Forms, Price Inequalities, and Benjamini–Schramm Convergence. arXiv:1909.05634v1 [math.DG]
do Carmo, M.P, : Riemannian Geometry Mathematics. Theory and Applications. Birkhäuser Boston Inc., Boston (1992)
Hamenstädt, U.: Small eigenvalues in thick-thin decomposition in negative curvature. Ann. Inst. Fourier (Grenoble) 69(7), 3065–3093 (2019)
Acknowledgements
The author would like to thank Professor Mark Stern for asking the question addressed in this paper, and for several early discussions regarding this matter. Finally, he thanks the two referees for useful and constructive comments.
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Di Cerbo, L.F. On the boundary injectivity radius of Buser–Colbois–Dodziuk-Margulis tubes. Ann Glob Anal Geom 59, 285–295 (2021). https://doi.org/10.1007/s10455-020-09750-5
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DOI: https://doi.org/10.1007/s10455-020-09750-5