scholarly journals Geodesic planes in geometrically finite manifolds-corrigendum

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Osama Khalil
Keyword(s):  
Geometrically Finite

scholarly journals Geodesic planes in geometrically finite acylindrical -manifolds

2021 ◽  
pp. 1-40
Author(s):  
YVES BENOIST ◽  
HEE OH
Keyword(s):  
Closed Geodesic ◽  
Duke Math ◽  
Geometrically Finite ◽  
Convex Cocompact ◽  
Invent Math ◽  
Convex Core

Abstract Let M be a geometrically finite acylindrical hyperbolic $3$ -manifold and let $M^*$ denote the interior of the convex core of M. We show that any geodesic plane in $M^*$ is either closed or dense, and that there are only countably many closed geodesic planes in $M^*$ . These results were obtained by McMullen, Mohammadi and Oh [Geodesic planes in hyperbolic 3-manifolds. Invent. Math.209 (2017), 425–461; Geodesic planes in the convex core of an acylindrical 3-manifold. Duke Math. J., to appear, Preprint, 2018, arXiv:1802.03853] when M is convex cocompact. As a corollary, we obtain that when M covers an arithmetic hyperbolic $3$ -manifold $M_0$ , the topological behavior of a geodesic plane in $M^*$ is governed by that of the corresponding plane in $M_0$ . We construct a counterexample of this phenomenon when $M_0$ is non-arithmetic.

scholarly journals Geometrically Finite Poincaré–Einstein Metrics

2020 ◽  
Vol 377 (3) ◽  
pp. 2159-2189
Author(s):  
Eric Bahuaud ◽  
Frédéric Rochon
Keyword(s):  
Einstein Metrics ◽  
Geometrically Finite

scholarly journals Maximally stretched laminations on geometrically finite hyperbolic manifolds

2017 ◽  
Vol 21 (2) ◽  
pp. 693-840 ◽  
Author(s):  
François Guéritaud ◽  
Fanny Kassel
Keyword(s):  
Hyperbolic Manifolds ◽  
Geometrically Finite
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