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In this paper we provide characterizations for the Gromov hyperbolicity of some particular Denjoy domains and besides some sufficient conditions to guarantee or discard the hyperbolicity of some others.
The conditions obtained involve just the lengths of some special simple closed geodesics in the domain. These results, on the one hand, show the extraordinary complexity of determining the hyperbolicity of a domain and, on the other hand, allow us to construct easily a large variety of both hyperbolic and non-hyperbolic domains.
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참고문헌 (31)
참고문헌 신청
A. Basmajian / 1990 / Constructing pairs of pants / Ann. Acad. Sci. Fenn. Ser. A I Math 15 (1) : 65 ~ 74
A. Basmajian / 1993 / Hyperbolic structures for surfaces of infinite type / Trans. Amer. Math. Soc 336 (1) : 421 ~ 444
A. Cant´on / 2001 / On harmonic functions on trees / Potential Anal 15 (3) : 199 ~ 244
A. F. Beardon / 1983 / The Geometry of Discrete Groups / Springer-Verlag
A. Haas / 1996 / Dirichlet points, Garnett points, and infinite ends of hyperbolic surfaces / I, Ann. Acad. Sci. Fenn. Math 21 (1) : 3 ~ 29
A. Basmajian / 1993 / Hyperbolic structures for surfaces of infinite type / Trans. Amer. Math. Soc 336 (1) : 421 ~ 444
A. Cant´on / 2001 / On harmonic functions on trees / Potential Anal 15 (3) : 199 ~ 244
A. F. Beardon / 1983 / The Geometry of Discrete Groups / Springer-Verlag
A. Haas / 1996 / Dirichlet points, Garnett points, and infinite ends of hyperbolic surfaces / I, Ann. Acad. Sci. Fenn. Math 21 (1) : 3 ~ 29
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