Conical limit points and groups of divergence type
Author:
Sungbok Hong
Journal:
Trans. Amer. Math. Soc. 346 (1994), 341-357
MSC:
Primary 22E40; Secondary 20H10
DOI:
https://doi.org/10.1090/S0002-9947-1994-1273535-1
MathSciNet review:
1273535
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We use the Patterson-Sullivan measure to generalize Agard's theorem to all groups of divergence type. As a consequence, we prove that for a nonelementary group of divergence type, the conical limit set has positive Patterson-Sullivan measure.
- [A] Stephen Agard, A geometric proof of Mostow’s rigidity theorem for groups of divergence type, Acta Math. 151 (1983), no. 3-4, 231–252. MR 723011, https://doi.org/10.1007/BF02393208
- [B] Alan F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer-Verlag, New York, 1983. MR 698777
- [B-M] Alan F. Beardon and Bernard Maskit, Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math. 132 (1974), 1–12. MR 333164, https://doi.org/10.1007/BF02392106
- [N] Peter J. Nicholls, The ergodic theory of discrete groups, London Mathematical Society Lecture Note Series, vol. 143, Cambridge University Press, Cambridge, 1989. MR 1041575
- [S] Dennis Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 171–202. MR 556586
Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E40, 20H10
Retrieve articles in all journals with MSC: 22E40, 20H10
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1994-1273535-1
Keywords:
Nonelementary group,
group of divergence type Patterson-Sullivan measure,
conical limit point
Article copyright:
© Copyright 1994
American Mathematical Society