Conformal Mapping and Brain Flattening

Murtagh, Stefano (2016) Conformal Mapping and Brain Flattening. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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In this dissertation we study some of the main results concerning conformal mappings in the complex plane and between Riemann surfaces and we apply those results to the so-called brain flattening problem. In the first part of this thesis we prove the Riemann Mapping Theorem and we provide an introduction to the Uniformization Theorem for simply connected Riemann surfaces. The second part of the thesis is focused on the brain flattening problem, which deals with how to construct a conformal mapping from the brain's cortical surface to the unitary sphere. This procedure leads to a possible definition of the discrete mean curvature on a triangulated closed surface of genus zero. This flattening method has several applications in neuroscience.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Murtagh, Stefano
Relatore della tesi
Corso di studio
Curriculum A: Generale e applicativo
Ordinamento Cds
Parole chiave
conformal mapping brain flattening Riemann Mapping Theorem Uniformization Theorem discrete mean curvature
Data di discussione della Tesi
16 Dicembre 2016

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