Geodesic
Convexity of balls in outer space
Yulan Qing1 ; Kasra Rafi2
1Fudan University, Shanghai, China
2University of Toronto, Canada
Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 893-934

Voir la notice de l'article provenant de la source EMS Press

DOI

In this paper we study the convexity properties of geodesics and balls in Outer space equipped with the Lipschitz metric. We introduce a class of geodesics called balanced folding paths and show that, for every loop α, the length of α along a balanced folding path is not larger than the maximum of its lengths at the endpoints. This implies that out-going balls are weakly convex. We then show that these results are sharp by providing several counter examples.
DOI : 10.4171/ggd/615
Classification : 20-XX, 00-XX
Mots-clés : Outer space, Out(Fn​), folding path

Yulan Qing  1   ; Kasra Rafi  2

1 Fudan University, Shanghai, China
2 University of Toronto, Canada 
Yulan Qing; Kasra Rafi. Convexity of balls in outer space. Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 893-934. doi: 10.4171/ggd/615
@article{10_4171_ggd_615,
     author = {Yulan Qing and Kasra Rafi},
     title = {Convexity of balls in outer space},
     journal = {Groups, geometry, and dynamics},
     pages = {893--934},
     year = {2021},
     volume = {15},
     number = {3},
     doi = {10.4171/ggd/615},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/615/}
}
TY  - JOUR
AU  - Yulan Qing
AU  - Kasra Rafi
TI  - Convexity of balls in outer space
JO  - Groups, geometry, and dynamics
PY  - 2021
SP  - 893
EP  - 934
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/615/
DO  - 10.4171/ggd/615
ID  - 10_4171_ggd_615
ER  - 
%0 Journal Article
%A Yulan Qing
%A Kasra Rafi
%T Convexity of balls in outer space
%J Groups, geometry, and dynamics
%D 2021
%P 893-934
%V 15
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/615/
%R 10.4171/ggd/615
%F 10_4171_ggd_615

Cité par Sources :