Shadow lemma on the product of Hadamard manifolds and applications

Françoise Dal’Bo[1]; Inkang Kim[2]

  • [1] Université de Rennes 1 Institut Mathématique de Rennes Campus de Beaulieu 35042 Rennes cedex (France)
  • [2] Seoul National University Department of Mathematics 151-742 KOREA

Séminaire de théorie spectrale et géométrie (2006-2007)

  • Volume: 25, page 105-119
  • ISSN: 1624-5458

Abstract

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In this paper we analyze the limit set of nonelementary subgroups acting by isometries on the product of two pinched Hadamard manifolds. Following M. Burger’s and P. Albuquerque’s works, we study the properties of Patterson-Sullivan’s measures on the limit sets of graph groups associated to convex cocompact groups.

How to cite

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Dal’Bo, Françoise, and Kim, Inkang. "Shadow lemma on the product of Hadamard manifolds and applications." Séminaire de théorie spectrale et géométrie 25 (2006-2007): 105-119. <http://eudml.org/doc/11218>.

@article{Dal2006-2007,
abstract = {In this paper we analyze the limit set of nonelementary subgroups acting by isometries on the product of two pinched Hadamard manifolds. Following M. Burger’s and P. Albuquerque’s works, we study the properties of Patterson-Sullivan’s measures on the limit sets of graph groups associated to convex cocompact groups.},
affiliation = {Université de Rennes 1 Institut Mathématique de Rennes Campus de Beaulieu 35042 Rennes cedex (France); Seoul National University Department of Mathematics 151-742 KOREA},
author = {Dal’Bo, Françoise, Kim, Inkang},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {limit set; graph groups; pinched Hadamard manifolds},
language = {eng},
pages = {105-119},
publisher = {Institut Fourier},
title = {Shadow lemma on the product of Hadamard manifolds and applications},
url = {http://eudml.org/doc/11218},
volume = {25},
year = {2006-2007},
}

TY - JOUR
AU - Dal’Bo, Françoise
AU - Kim, Inkang
TI - Shadow lemma on the product of Hadamard manifolds and applications
JO - Séminaire de théorie spectrale et géométrie
PY - 2006-2007
PB - Institut Fourier
VL - 25
SP - 105
EP - 119
AB - In this paper we analyze the limit set of nonelementary subgroups acting by isometries on the product of two pinched Hadamard manifolds. Following M. Burger’s and P. Albuquerque’s works, we study the properties of Patterson-Sullivan’s measures on the limit sets of graph groups associated to convex cocompact groups.
LA - eng
KW - limit set; graph groups; pinched Hadamard manifolds
UR - http://eudml.org/doc/11218
ER -

References

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  1. P. Albuquerque, Patterson-Sullivan theory in higher rank symmetric spaces, Geom. Funct. Anal. 9 (1999), 1-28 Zbl0954.53031MR1675889
  2. Y. Benoist, Propriétés asymptotiques des groupes linéaires, Geom. Funct. Anal. 7 (1997), 1-47 Zbl0947.22003MR1437472
  3. Marc Bourdon, Structure conforme au bord et flot géodésique d’un CAT ( - 1 ) -espace, Enseign. Math. (2) 41 (1995), 63-102 Zbl0871.58069
  4. Marc Burger, Intersection, the Manhattan curve, and Patterson-Sullivan theory in rank 2 , Internat. Math. Res. Notices (1993), 217-225 Zbl0829.57023MR1230298
  5. Françoise Dal’bo, Géométrie d’une famille de groupes agissant sur le produit de deux variétés d’Hadamard, Séminaire de Théorie Spectrale et Géométrie, No. 15, Année 1996–1997 15 (1997), 85-98, Univ. Grenoble I, Saint Zbl0898.53027
  6. Françoise Dal’bo, Remarques sur le spectre des longueurs d’une surface et comptages, Bol. Soc. Brasil. Mat. (N.S.) 30 (1999), 199-221 Zbl1058.53063
  7. Françoise Dal’Bo, Inkang Kim, A criterion of conjugacy for Zariski dense subgroups, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), 647-650 Zbl0953.22013
  8. Françoise Dal’Bo, Inkang Kim, Marked length rigidity for symmetric spaces, Comment. Math. Helv. 77 (2002), 399-407 Zbl1002.22005
  9. Françoise Dal’bo, Marc Peigné, Some negatively curved manifolds with cusps, mixing and counting, J. Reine Angew. Math. 497 (1998), 141-169 Zbl0890.53043
  10. Étienne Ghys, Pierre de la Harpe, La propriété de Markov pour les groupes hyperboliques, Sur les groupes hyperboliques d’après Mikhael Gromov (Bern, 1988) 83 (1990), 165-187, Birkhäuser Boston, Boston, MA Zbl0731.20025
  11. Yves Guivarc’h, Produits de matrices aléatoires et applications aux propriétés géométriques des sous-groupes du groupe linéaire, Ergodic Theory Dynam. Systems 10 (1990), 483-512 Zbl0715.60008
  12. Ernst Heintze, Hans-Christoph Im Hof, Geometry of horospheres, J. Differential Geom. 12 (1977), 481-491 (1978) Zbl0434.53038MR512919
  13. Inkang Kim, Ergodic theory and rigidity on the symmetric space of non-compact type, Ergodic Theory Dynam. Systems 21 (2001), 93-114 Zbl0978.37016MR1826662
  14. Inkang Kim, Marked length rigidity of rank one symmetric spaces and their product, Topology 40 (2001), 1295-1323 Zbl0997.53034MR1867246
  15. Inkang Kim, Rigidity on symmetric spaces, Topology 43 (2004), 393-405 Zbl1049.53031MR2052969
  16. Inkang Kim, Isospectral finiteness on hyperbolic 3-manifolds, Comm. Pure Appl. Math. 59 (2006), 617-625 Zbl1102.53028MR2172803
  17. Gabriele Link, Limit sets of discrete groups acting on symmetric spaces, (2002) 
  18. Peter J. Nicholls, The ergodic theory of discrete groups, 143 (1989), Cambridge University Press, Cambridge Zbl0674.58001MR1041575
  19. J. F. Quint, Sous-groupes discrets des groupes de Lie semi-simples réels et p-adiques, (2001) 

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