Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Generalizing The Hyperbolic Collar Lemma

Author(s): Ara Basmajian
Journal: Bull. Amer. Math. Soc. 27 (1992), 154-158.
MSC (1991): Primary 30F40, 53C20
MathSciNet review: 1145576
Retrieve article in: PDF

References | Similar articles | Additional information

References:

[Ap]
Boris Apanasov, Discrete groups in space and uniformization problems, Kluwer Academic, Dordrecht, Netherlands, 1991. MR 1191903
[ Ba1]
Ara Basmajian, Constructing pairs of pants, Ann. Acad. Sci. Fenn. Ser. A I Math. \textbf{15} (1990), 65--74. MR 1050782
[ Ba2]
Ara Basmajian, The orthogonal spectrum of a hyperbolic manifold, Amer. J. Math., (to appear, 1992). MR 1246187
[ Ba3]
Ara Basmajian, The stable neighborhood theorem and lengths of closed geodesics, Proc. Amer. Math. Soc., (to appear). MR 1152271
[ Ba4]
Ara Basmajian, Tubular neighborhoods of totally geodesic hypersurfaces in hyperbolic manifolds, preprint. MR 1273264
[ Be]
Lipman Bers, An inequality for Riemann surfaces, Differential geometry and Complex analysis, H.E. Rauch Memorial volume (Isaac Chavel and Herschel M. Farkas, eds.), Springer-Verlag, New York, 1985, pp. 87--93. MR 780038
[ Bu]
Peter Buser, The collar theorem and examples, Manuscripta Math. \textbf{25} (1978), 349-357. MR 509590
[ Ha]
N. Halpern, A proof of the collar lemma, Bull. London Math. Soc. \textbf{13} (1981), 141--144. MR 608099
[ He]
John Hempel, Traces, lengths, and simplicity of loops on surfaces, Topology Appl. \textbf{18} (1984), 153--161. MR 769288
[ Jo]
Troels Jorgensen, on discrete groups of M\"obius transformations, Amer. J. Math. \textbf{98} (1976), 739--749. MR 427627
[ Ke]
Linda Keen, Collars on Riemann surfaces, Discontinuous Groups and Riemann Surfaces, Ann. of Math. Stud., vol. 79, Princeton Univ. Press, Princeton, NJ, 1974, pp. 263--268. MR 379833
[ KM]
S. Kojima and Y. Miyamoto, The smallest hyperbolic 3-manifolds with totally geodesic boundary, J. Differential Geometry \textbf{34} (1991), 175--192. MR 1114459
[ Ma1]
Bernard Maskit, Comparison of hyperbolic and extremal lengths, Ann. Acad. Sci. Fenn. Ser. A I Math. \textbf{10} (1985), 381--386. MR 802500
[ Ma2]
Bernard Maskit, Kleinian groups, Springer-Verlag, New York, 1988. MR 959135
[ Mt]
Peter Matelski, A compactness theorem for Fuchsian groups of the second kind, Duke Math. J. \textbf{43} (1976), 829--840. MR 432921
[ Me]
Bob Meyerhoff, A lower bound for the volume of hyperbolic \RM 3-manifolds, Canad. J. Math. \textbf{39} (1987), 1038--1056. MR 918586
[ N]
Toshihiro Nakanishi, The lengths of the closed geodesics on a Riemann surface with self-intersection, Tohoku Math. J. (2) \textbf{41} (1989), 527--541. MR 1025320
[ R]
Burton Randol, Cylinders in Riemann surfaces, Comment. Math. Helv. \textbf{54} (1979), 1--5. MR 522028
[ Th]
William Thurston, The geometry and topology of \RM 3-manifolds, lecture notes, Princeton University, 1977. MR
[ Y1]
Akira Yamada, On Marden's universal constant of Fuchsian groups, Kodai Math. J. \textbf{4} (1981), 266--277. MR 630246
[ Y2]
Akira Yamada, On Marden's universal constant of Fuchsian groups {\rm II}, J. Analyse Math. \textbf{41} (1982), 234--248. MR 687954

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1991): 30F40, 53C20

Retrieve articles in all Journals with MSC (1991): 30F40, 53C20


Additional Information:

DOI: 10.1090/S0273-0979-1992-00298-7
PII: S 0273-0979(1992)00298-7