Riemann Surfaces

Ahlfors, Lars V.; Sario, Leo

doi:10.1515/9781400874538

Cited by 526 publications

(98 citation statements)

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“…We always consider DX with its intrinsic distance with respect to this L. If X = S is a bordered surface and ∂S = ∪ j∈J η j , DS is known as the Schottky double of S (see e.g. [1], p.119).…”

Section: Results In Metric Spacesmentioning

confidence: 99%

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Gromov hyperbolicity of Denjoy Domains

et al. 2006

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Abstract. In this paper we characterize the Gromov hyperbolicity of the double of a metric space. This result allows to give a characterization of the hyperbolic Denjoy domains, in terms of the distance to R of the points in some geodesics. In the particular case of trains (a kind of Riemann surfaces which includes the flute surfaces), we obtain more explicit criteria which depend just on the lengths of what we have called fundamental geodesics.

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Section: Results In Metric Spacesmentioning

confidence: 99%

“…We also have that the points in [b 1 , c] and in [c, a 1 ] are at distance least or equal than 4δ 0 . Hence, T is (…”

Section: Results In Metric Spacesmentioning

confidence: 99%

Gromov hyperbolicity of Denjoy Domains

et al. 2006

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“…• Proof. Canonical form of Y (see [3], p. 94) is (let us say) with p handles and q contours i.e., by cutting out 2p + q discs out of the Riemann sphere and then attaching p handles by pairing off 2p of the holes, we get a homeomorph of Y.…”

Section: H T (Y L< >)mentioning

confidence: 99%

A note on real orthogonal measures

Ahern¹,

Rao²

1981

Pacific J. Math.

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“…It is said to be complete (cf. [2]) if every a ∈ Y has a closed parametric disc K around a such that each component of f −1 (K) is compact. When (X, Y, f ) is smooth, i.e.…”

Section: §1 Introductionmentioning

confidence: 99%

Types of complete Infinitely sheeted Planes

Nakai¹

2004

Nagoya Mathematical Journal

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Abstract. We will answer negatively to the question whether the completeness of infinitely sheeted covering surfaces of the extended complex plane have anything to do with their types being parabolic or hyperbolic. This will be accomplished by giving a one parameter family {W [α] : α ∈ A} of complete infinitely sheeted planes W [α] depending on the parameter set A of sequences α = (an) n≥1 of real numbers 0 < an ≤ 1/2 (n ≥ 1) such that W [α] is parabolic for 'small' α's and hyperbolic for 'large' α's.

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Riemann Surfaces

Cited by 526 publications

References 0 publications

Gromov hyperbolicity of Denjoy Domains

Gromov hyperbolicity of Denjoy Domains

A note on real orthogonal measures

Types of complete Infinitely sheeted Planes

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