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ETD

Digital archive of theses discussed at the University of Pisa

 

Thesis etd-02142013-003146


Thesis type
Tesi di dottorato di ricerca
Author
MARCHESE, ANDREA
URN
etd-02142013-003146
Thesis title
Two applications of the Theory of Currents
Academic discipline
MAT/05
Course of study
MATEMATICA
Supervisors
tutor Prof. Alberti, Giovanni
Keywords
  • currents
  • Lipschitz functions
  • Steiner problem
Graduation session start date
15/02/2013
Availability
Full
Summary
In the first part of the thesis we find an adapted version of the Rademacher theorem of differentiability of Lipschitz functions, when the Lebesgue measure on the euclidean space is replaced by a generical Radon measure.

In the second part of the thesis we explain how to understand the Steiner tree problem as a mass minimization problem in a family of rectifiable currents with coefficients in a normed group and we exhibit some calibrations in order to prove the absolute minimaity of some concrete configurations.

The common point of this problems is a substantial use of the Theory of Currents as a tool for proofs
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