Surface groups acting on CAT(-1) spaces
Harmonic map theory is used to show that a convex cocompact surface group action on a - - - $\text{CAT}(-1)$ - - - metric space fixes a convex copy of the hyperbolic plane (i.e. the action is Fuchsian) if and only if the Hausdorff dimension of the limit set of the action is equal to 1. This pr...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
2019
|
| In: |
Ergodic theory and dynamical systems
Year: 2017, Volume: 39, Issue: 7, Pages: 1843-1856 |
| ISSN: | 1469-4417 |
| DOI: | 10.1017/etds.2017.103 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1017/etds.2017.103 Verlag, Volltext: https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/surface-groups-acting-on-textcat1-spaces/26F8A4B6AE66B734EA769C42A301E353 
|
| Author Notes: | Georgios Daskalopoulos, Chikako Mese, Andrew Sanders and Alina Vdovina |
| Summary: | Harmonic map theory is used to show that a convex cocompact surface group action on a - - - $\text{CAT}(-1)$ - - - metric space fixes a convex copy of the hyperbolic plane (i.e. the action is Fuchsian) if and only if the Hausdorff dimension of the limit set of the action is equal to 1. This provides another proof of a result of Bonk and Kleiner. More generally, we show that the limit set of every convex cocompact surface group action on a - - - $\text{CAT}(-1)$ - - - space has Hausdorff dimension - - - $\geq 1$ - - - , where the inequality is strict unless the action is Fuchsian. |
|---|---|
| Item Description: | Published online by Cambridge University Press: 04 December 2017 "CAT(-1)" ist im Titel gesetzt in anderer Type als der übrige Text Gesehen am 29.11.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1469-4417 |
| DOI: | 10.1017/etds.2017.103 |