Commentarii Mathematici Helvetici
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Quasi-isometries of groups, graphs and surfacesSylvain Maillot (1) Institut de Mathématiques et de Modélisation, Université Montpellier II, Case Courrier 051, Place Eugène Bataillon, 34095, MONTPELLIER CEDEX, FRANCE
We give a characterization of virtual surface groups as groups quasi-isometric to complete simply-connected Riemannian surfaces. Results on the equivalence up to quasi-isometry of various bounded geometry conditions for Riemannian surfaces are also obtained.
Keywords: Quasi-isometry, surface group, free group, isoperimetric inequality.
Maillot Sylvain: Quasi-isometries of groups, graphs and surfaces. Comment. Math. Helv. 76 (2001), 29-60. doi: 10.1007/s000140050149