Marzo Sánchez, JordiVilaseca Vinadé, Guillem2025-07-182025-07-182025-01-15https://hdl.handle.net/2445/222361Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Jordi Marzo SánchezThe main goal of this work is to give an introduction of the fundamental concepts in complex analysis in several variables. It starts by introducing holomorphic functions of several complex variables, their representation via power series, and fundamental results like the Cauchy integral formula. Then it follows by the Riemann mapping theorem, a cornerstone result that guarantees the existence of conformal mappings between simply connected domains and the unit disc in $\mathbb{C}$. We show also that the Riemann mapping theorem cannot be extended to $\mathbb{C}^n$. Finally, the last part of the report delves into Bergman spaces, studying their kernels and their connection to the Riemann Mapping Theorem.46 p.application/pdfengcc-by-nc-nd (c) Guillem Vilaseca Vinadé, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/es/Funcions de diverses variables complexesNuclis de BergmanTeoria geomètrica de funcionsFuncions holomorfesTreballs de fi de grauFunctions of several complex variablesBergman kernel functionsGeometric function theoryHolomorphic functionsBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess