本論文介紹Teichmuller 空間的參數化方法。我們會就此題目會作一歷史回顧，然後介紹Fenchel-Nielsen的參數化方法，最後集中討論在緊密且有界之曲面上的Teichmuller 空間以六角形分割之參數化方法。 / This thesis is an exposition of different parametrizations of the Teichmuller space. We will give a historical review on this subject, and in particular introduce the Fenchel-Nielsen coordinate. Our main focus would be the cellular decomposition method to parametrize the Teichmuller spaces of compact surface with boundary. / Detailed summary in vernacular field only. / Wong, Yun Shun Matthias. / "October 2012." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 42-43). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Teichmüller Space --- p.4 / Chapter 2.1 --- Definition of Teichmüller Space --- p.4 / Chapter 2.2 --- Historical review --- p.6 / Chapter 3 --- Fenchel-Nielsen Coordinate --- p.10 / Chapter 4 --- Cellular Decomposition Method --- p.18 / Chapter 4.1 --- Ideal Triangulation --- p.19 / Chapter 4.2 --- Edge Invariant --- p.22 / Chapter 4.2.1 --- E-Invariant of Colored Hexagon --- p.23 / Chapter 4.3 --- E-coordinate and its Generalization --- p.24 / Chapter 4.4 --- Edge Path and Edge Cycle --- p.26 / Chapter 4.5 --- Parametrization Theorems --- p.26 / Chapter 4.6 --- Discussion on the Results --- p.30 / Chapter 4.7 --- The Variational Proof of Theorem 4.8 --- p.32 / Chapter 4.7.1 --- Overview of the Proof --- p.32 / Chapter 4.7.2 --- The Energy Function on Hexagon --- p.35 / Chapter 4.7.3 --- The Energy Function on Length Structure and the Proof of Theorem 4.8 --- p.37 / Bibliography --- p.42
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328618 |
| Date | January 2013 |
| Contributors | Wong, Yun Shun Matthias., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (vi, 43 leaves) : ill. (chiefly col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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