Geodesic
Length functions in Teichmüller and anti-de Sitter geometry
Forum of Mathematics, Sigma, Tome 11 (2023)

Voir la notice de l'article provenant de la source Cambridge University Press

We establish a link between the behavior of length functions on Teichmüller space and the geometry of certain anti-de Sitter $3$-manifolds. As an application, we give new purely anti-de Sitter proofs of results of Teichmüller theory such as (strict) convexity of length functions along shear paths and geometric bounds on their second variation along earthquakes. Along the way, we provide shear-bend coordinates for GHMC anti-de Sitter $3$-manifolds. 
@article{10_1017_fms_2023_100,
     author = {Filippo Mazzoli and Gabriele Viaggi},
     title = {Length functions in {Teichm\"uller} and anti-de {Sitter} geometry},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {11},
     year = {2023},
     doi = {10.1017/fms.2023.100},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.100/}
}
TY  - JOUR
AU  - Filippo Mazzoli
AU  - Gabriele Viaggi
TI  - Length functions in Teichmüller and anti-de Sitter geometry
JO  - Forum of Mathematics, Sigma
PY  - 2023
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.100/
DO  - 10.1017/fms.2023.100
LA  - en
ID  - 10_1017_fms_2023_100
ER  - 
%0 Journal Article
%A Filippo Mazzoli
%A Gabriele Viaggi
%T Length functions in Teichmüller and anti-de Sitter geometry
%J Forum of Mathematics, Sigma
%D 2023
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.100/
%R 10.1017/fms.2023.100
%G en
%F 10_1017_fms_2023_100
Filippo Mazzoli; Gabriele Viaggi. Length functions in Teichmüller and anti-de Sitter geometry. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.100

Cité par Sources :