Essays about: "holomorphic functions"

Found 5 essays containing the words holomorphic functions.

  1. 1. The Uniformization Theorem

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Nikita Zozoulenko; [2021]
    Keywords : complex analysis; riemann surface; analytic functions; holomorphic functions; differential geometry; harmonic; subharmonic; perron; analysis; Mathematics and Statistics;

    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

  3. 2. A Comparison Of Harmonic And Holomorphic Functions

    University essay from Mälardalens högskola/Akademin för utbildning, kultur och kommunikation

    Author : Adrian Daniel Renz; [2020]
    Keywords : harmonic; holomoephic; analysis;

    Abstract : Many results in real and complex analysis are the consequence of mean value properties and theorems. This is the case for harmonic and holomorphic functions as well. The mean value property builds the foundation for several properties of each set of functions. READ MORE

  4. 3. The Existence of Meromorphic Functions with Prescribed Poles and Principal Parts

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Peicen Liu; [2020]
    Keywords : The Mittag-Leffler Theorem; Meromorphic Function; Complex Analysis; The Mittag-Leffler Star; Mathematics and Statistics;

    Abstract : The Swedish mathematician Gösta Mittag-Leffler (1846-1927) is well-known for founding Acta Mathematica, the famous international mathematical journal. His mathematical contributions are connected chiefly with complex analysis. READ MORE

  5. 4. The Oka-Weil Theorem

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Jesper Karlsson; [2017]
    Keywords : several complex variables; holomorphic functions; polynomial convexity; Oka-Weil theorem; Oka extension theorem; differential forms;

    Abstract : We give a proof of the Oka-Weil theorem which states that on compact, polynomially convex subsets of Cn, holomorphic functions can be approximated uniformly by holomorphic polynomials. ... READ MORE

  6. 5. Algorithmic Construction of Fundamental Polygons for Certain Fuchsian Groups

    University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Author : David Larsson; [2015]
    Keywords : Compact Riemann surfaces and uniformization; Fuchsian groups and automorphic functions; Hyperbolic geometry; Topological groups; Permutation groups; Computational methods; Covering spaces; branched coverings; Generators; relations; and presentations;

    Abstract : 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