论文标题
紫红色的猫（-1）表面组表示
Dominating CAT(-1) surface group representations by Fuchsian ones
论文作者
论文摘要
We show that for every representation $ ρ: π_{1} (S_{g}) \to \text{Isom}(X) $ of the fundamental group of a genus $ g \ge 2 $ surface to the isometry group of a complete $ \text{CAT}(-1) $ metric space $ X $ there exists a Fuchsian representation $ j $ and a $ (j, ρ) $ - equivariant地图来自$ \ mathbb {h}^{2} $ to $ x $，是$ c $ -lipschitz，对于某些$ c <1 $，或$ρ$限制到紫红色表示。这概括了Gueritaud-Kassel-Wolff，Deroin-Tholozan和Daskalopoulos-Mese-Sanders-Sanders-Vdovina的结果
We show that for every representation $ ρ: π_{1} (S_{g}) \to \text{Isom}(X) $ of the fundamental group of a genus $ g \ge 2 $ surface to the isometry group of a complete $ \text{CAT}(-1) $ metric space $ X $ there exists a Fuchsian representation $ j $ and a $ (j, ρ) $-equivariant map from $ \mathbb{H}^{2} $ to $ X $ which is $ c $ -Lipschitz for some $ c < 1 $, or $ ρ$ restricts to a Fuchsian representation. This generalizes results of Gueritaud-Kassel-Wolff, Deroin-Tholozan and Daskalopoulos-Mese-Sanders-Vdovina
