Rodríguez Otero, Candela2026-05-272026-05-272024-06https://hdl.handle.net/10347/4742648 páxinasO obxectivo deste traballo é contextualizar, enunciar e demostrar algúns dos teoremas máis relevantes da teoría global de curvas planas desde a perspectiva da xeometría diferencial. Así, abordaremos o estudo da Umlaufsatz de Hopf, o teorema da curva pechada de Jordan, a desigualdade isoperimétrica, o teorema de Fenchel e o teorema dos catro vértices. Despois dunha breve introdución aos conceptos básicos da xeometría diferencial de curvas planas, presentaremos as ferramentas necesarias para o estudo de cada un dos resultados mencionados, para finalmente proporcionar unha proba de cada un deles. Tales probas serán eminentemente xeométricas, se ben en varios casos contarán cunha compoñente topolóxica e analítica importante.The objective of this work is to contextualize, state and prove some of the most relevant theorems of the global theory of plane curves from a differential geometry perspective. Thus, we will address the study of Hopf's Umlaufsatz, Jordan's closed curve theorem, the isoperimetric inequality, Fenchel's theorem and the four-vertex theorem. After a short introduction to the basic concepts of differential geometry of plane curves, we will present the necessary tools for the study of each of the mentioned results, to finally provide a proof of each of them. Such proofs will be eminently geometric, although in several cases they will have an important topological and analytical component.glgAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/bachelor thesisopen access