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http://hdl.handle.net/2445/151979
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DC Field | Value | Language |
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dc.contributor.advisor | Massaneda Clares, Francesc Xavier | - |
dc.contributor.author | Roig Sanchis, Anna | - |
dc.date.accessioned | 2020-03-04T11:13:57Z | - |
dc.date.available | 2020-03-04T11:13:57Z | - |
dc.date.issued | 2019-06-19 | - |
dc.identifier.uri | http://hdl.handle.net/2445/151979 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Francesc Xavier Massaneda Clares | ca |
dc.description.abstract | [en] In this work, we will study the theory holomorphic and univalent functions in proper simply connected domains of $\mathbb{C}$; in particular on the case where the domain is the unit disk. We will expose the most important results of the theory, and focus especially on one of its major problems: the Bierberbach conjecture (BC), stated in 1916 by Ludwig Bieberbach, and proved in 1984 by Louis de Branges, which claims: Bieberbach's Conjecture. The coefficients of each analytic and univalent function $f(z)=$ $z+\sum_{n=2}^{\infty} a_{n} z^{n}$ in the unit disk, with $f(0)=0$ and $f^{\prime}(0)=1$ satisfy: $$ \left|a_{n}\right| \leq n, \quad \text { for } \quad n=2,3, \cdots $$ Strict inequality holds for every n unless $f$ is a rotation of the Koebe function. | ca |
dc.format.extent | 60 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Anna Roig Sanchis, 2019 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Funcions univalents | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Funcions de variables complexes | ca |
dc.subject.classification | Teoria geomètrica de funcions | ca |
dc.subject.other | Univalent functions | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Functions of complex variables | en |
dc.subject.other | Geometric function theory | en |
dc.title | Univalent functions. The Bieberbach conjecture | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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151979.pdf | Memòria | 672.84 kB | Adobe PDF | View/Open |
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