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Some Theorems in Kleinian Groups and Complex Dynamics
Başlık:
Some Theorems in Kleinian Groups and Complex Dynamics
Yazar:
He, Yan Mary, author. (orcid)0000-0002-0729-7711
ISBN:
9780438092549
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (65 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Danny Calegari; Peter B. Shalen.
Özet:
This thesis is an amalgam of the two manuscripts [16] and [17] that the author completed during her graduate studies at the University of Chicago. Article [16] was published in Ergodic Theory and Dynamical Systems and is reprinted with permission here.
The first part of the thesis contains results obtained in [16], where we study Basmajian-type series identities on holomorphic families of Cantor sets associated to one-dimensional complex dynamical systems. We show that the series is absolutely summable if and only if the Hausdorff dimension of the Cantor set is strictly less than one. Throughout the domain of convergence, these identities can be analytically continued and they exhibit nontrivial monodromy.
The second part of the thesis follows mainly from [17]. In particular, we prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the log(2 k - 1) Theorem for Kleinian groups due to Anderson- Canary-Culler-Shalen [1]. As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as the two-dimensional Margulis constant and lengths of a pair of based loops, which improves a result of Buser's.
Notlar:
School code: 0330
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(691366.1) | 691366-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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