Geodesic
Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives
Bromberg, K.1, 2
1 Department of Mathematics, California Institute of Technology, Pasadena, California 91125
2 Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Journal of the American Mathematical Society, Tome 17 (2004) no. 4, pp. 783-826

Voir la notice de l'article provenant de la source American Mathematical Society

Given a geometrically finite hyperbolic cone-manifold, with the cone-singularity sufficiently short, we construct a one-parameter family of cone-manifolds decreasing the cone-angle to zero. We also control the geometry of this one-parameter family via the Schwarzian derivative of the projective boundary and the length of closed geodesics.
DOI : 10.1090/S0894-0347-04-00462-X

Bromberg, K. 1, 2

1 Department of Mathematics, California Institute of Technology, Pasadena, California 91125
2 Department of Mathematics, University of Utah, Salt Lake City, Utah 84112 
@article{10_1090_S0894_0347_04_00462_X,
     author = {Bromberg, K.},
     title = {Hyperbolic cone-manifolds, short geodesics, and {Schwarzian} derivatives},
     journal = {Journal of the American Mathematical Society},
     pages = {783--826},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2004},
     doi = {10.1090/S0894-0347-04-00462-X},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-04-00462-X/}
}
TY  - JOUR
AU  - Bromberg, K.
TI  - Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives
JO  - Journal of the American Mathematical Society
PY  - 2004
SP  - 783
EP  - 826
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-04-00462-X/
DO  - 10.1090/S0894-0347-04-00462-X
ID  - 10_1090_S0894_0347_04_00462_X
ER  - 
%0 Journal Article
%A Bromberg, K.
%T Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives
%J Journal of the American Mathematical Society
%D 2004
%P 783-826
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-04-00462-X/
%R 10.1090/S0894-0347-04-00462-X
%F 10_1090_S0894_0347_04_00462_X
Bromberg, K. Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives. Journal of the American Mathematical Society, Tome 17 (2004) no. 4, pp. 783-826. doi: 10.1090/S0894-0347-04-00462-X

[1] Anderson, James W., Canary, Richard D. Cores of hyperbolic 3-manifolds and limits of Kleinian groups Amer. J. Math. 1996 745 779

[2] Anderson, James W., Canary, Richard D. Cores of hyperbolic 3-manifolds and limits of Kleinian groups. II J. London Math. Soc. (2) 2000 489 505

[3] Ballmann, Werner, Gromov, Mikhael, Schroeder, Viktor Manifolds of nonpositive curvature 1985

[4] Bers, Lipman On boundaries of Teichmüller spaces and on Kleinian groups. I Ann. of Math. (2) 1970 570 600

[5] Brock, Jeffrey, Bromberg, Kenneth, Evans, Richard, Souto, Juan Tameness on the boundary and Ahlfors’ measure conjecture Publ. Math. Inst. Hautes Études Sci. 2003 145 166

[6] Bromberg, K. Rigidity of geometrically finite hyperbolic cone-manifolds Geom. Dedicata 2004 143 170

[7] Canary, R. D. The conformal boundary and the boundary of the convex core Duke Math. J. 2001 193 207

[8] Canary, Richard D., Culler, Marc, Hersonsky, Sa’Ar, Shalen, Peter B. Approximation by maximal cusps in boundaries of deformation spaces of Kleinian groups J. Differential Geom. 2003 57 109

[9] Canary, R. D., Epstein, D. B. A., Green, P. Notes on notes of Thurston 1987 3 92

[10] Canary, Richard D., Minsky, Yair N. On limits of tame hyperbolic 3-manifolds J. Differential Geom. 1996 1 41

[11] Hodgson, Craig D., Kerckhoff, Steven P. Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery J. Differential Geom. 1998 1 59

[12] Hodgson, Craig D., Kerckhoff, Steven P. Harmonic deformations of hyperbolic 3-manifolds 2003 41 73

[13] Kodani, Shigeru Convergence theorem for Riemannian manifolds with boundary Compositio Math. 1990 171 192

[14] Kojima, Sadayoshi Deformations of hyperbolic 3-cone-manifolds J. Differential Geom. 1998 469 516

[15] Mcmullen, Curt Cusps are dense Ann. of Math. (2) 1991 217 247

[16] Otal, Jean-Pierre Les géodésiques fermées d’une variété hyperbolique en tant que nœuds 2003 95 104

[17] Wu, Hung Hsi The Bochner technique in differential geometry Math. Rep. 1988

Cité par Sources :