RT Journal Article
T1 Stability of the volume growth rate under quasi-isometries
A1 Granados, Ana
A1 Pestana Galván, Domingo de Guzmán
A1 Portilla, Ana
A1 Rodríguez García, José Manuel
A1 Tourís, Eva
AB Kanai proved powerful results on the stability under quasi-isometries of numerous global properties (including the volume growth rate) between non-bordered Riemannian manifolds of bounded geometry. Since his work focuses more on the generality of the spaces considered than on the two-dimensional geometry, Kanai's hypotheses are not usually satisfied in the context of Riemann surfaces endowed with the Poincaré metric. In this work we try to fill that gap and prove the stability of the volume growth rate by quasi-isometries, under hypotheses that many bordered or non-bordered Riemann surfaces (and even Riemannian surfaces with pinched negative curvature) satisfy. In order to get our results, it is shown that many bordered Riemannian surfaces with pinched negative curvature are bilipschitz equivalent to bordered surfaces with constant negative curvature.
PB Springer Nature
SN 1139-1138
YR 2020
FD 2020-01
LK https://hdl.handle.net/10016/38293
UL https://hdl.handle.net/10016/38293
LA eng
NO Supported in part by two grants from Ministerio de Economía y Competititvidad, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT), Spain.
DS e-Archivo
RD 17 jul. 2024