Essays about: "uniformization"
Found 5 essays containing the word uniformization.
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1. Hyperbolic fillings of bounded metric spaces
University essay from Linköpings universitet/Analys och didaktik; Linköpings universitet/Tekniska fakultetenAbstract : The aim of this thesis is to expand on parts of the work of Björn–Björn–Shanmugalingam [2] and in particular on the construction and properties of hyperbolic fillings of nonempty bounded metric spaces. In light of [2], we introduce two new parameters λ and ξ to the construction while relaxing a specific maximal-condition. READ MORE
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2. Markov Chains as a Real-time System Monitoring Service : Numerical Repair Rate Optimization (RRO)
University essay from Mälardalens universitet/Akademin för innovation, design och teknikAbstract : The expansion and increased complexity of technology is undoubtedly consistent and one can intuitively suppose that this trajectory will not deviate from this course in the years to come. On a continuous basis, concepts that started of as some hypothetical or abstract notions without practical relevance gets transferred to the modern state of our current technology. READ MORE
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3. The Uniformization Theorem
University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : In this bachelor's thesis we provide a self contained proof of the Uniformization Theorem. It states that a simply connected Riemann surface is conformally equivalent to either the complex plane C, the unit disk D, or the Riemann sphere C^*. READ MORE
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4. Algorithmic Construction of Fundamental Polygons for Certain Fuchsian Groups
University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakultetenAbstract : The work of mathematical giants, such as Lobachevsky, Gauss, Riemann, Klein and Poincaré, to name a few, lies at the foundation of the study of the highly structured Riemann surfaces, which allow definition of holomorphic maps, corresponding to analytic maps in the theory of complex analysis. A topological result of Poincaré states that every path-connected Riemann surface can be realised by a construction of identifying congruent points in the complex plane, the Riemann sphere or the hyperbolic plane; just three simply connected surfaces that cover the underlying Riemann surface. READ MORE
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5. On Poicarés Uniformization Theorem
University essay from Matematiska institutionenAbstract : A compact Riemann surface can be realized as a quotient space $\mathcal{U}/\Gamma$, where $\mathcal{U}$ is the sphere $\Sigma$, the euclidian plane $\mathbb{C}$ or the hyperbolic plane $\mathcal{H}$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal{U}\rightarrow\mathcal{U}/\Gamma$. READ MORE
