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tfg_blesa_bernat_pol.pdf (647.78 KB)

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Bachelor thesis

Publication date

2022-06-13

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cc-by-nc-nd (c) Bernat Pol Blesa, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/192362

Isoperimetric inequalities in the plane

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Abstract

[en] The main goal of this work is to study different geometric inequalities in the plane. In particular, we will work on the isoperimetric, the Saint-Venant and the Faber-Krahn inequalities for simple connected domains. We will use two different approaches: first a classic one by complex analysis, and then a more recent one by operator theory, bounding the commutator of Toeplitz operators in the HardySmirnov space $E_2$ and the Bergman space $A^2$. We will also study these spaces and how they relate with geometric quantities. Finally, we will talk about functions of bounded variation in order to extend the classical isoperimetric inequality for any domain in the plane.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Joaquim Ortega Cerdà

Subject

Desigualtats isoperimètriques, Treballs de fi de grau, Anàlisi matemàtica, Funcions de variables complexes, Espais de Hardy

Subject (English)

Isoperimetric inequalities, Bachelor's theses, Mathematical analysis, Functions of complex variables, Hardy spaces

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

POL BLESA, Bernat. Isoperimetric inequalities in the plane. [consulted: 7 of August of 2026]. Available at: https://hdl.handle.net/2445/192362

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