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Girotto, Nicola (2019) Minimizing Clusters : existence and planar examples. [Magistrali biennali]

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Abstract

The problem of enclosing a fixed area inside a figure in the plane with least perimeter was known since the times of ancient Greeks. They knew that the optimal solution was a circle, although they did not prove this fact precisely but just by approximation. Surprisingly, the first rigorous proof was found only in the 19th century. First Steiner showed that, if a solution exists, then it is necessarily a ball and, some years later, Carathéodory completed the proof showing the existence of the minimizers. We could generalize this problem, for example, trying to find two sets of fixed areas which minimize the perimeter of their boundary. In general, this problem could be set with N subsets of R n . This is called partitioning problem.

Item Type:Magistrali biennali
Corsi di Diploma di Laurea:Scuola di Scienze > Matematica
Uncontrolled Keywords:Cluster minimizing, perimeter, bubble
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Codice ID:62990
Relatore:Monti, Roberto
Data della tesi:27 September 2019
Biblioteca:Polo di Scienze > Biblioteca di Matematica

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