‌

Geometric Measure Theory

Period of duration of course
‌‌
Course info
Number of course hours
40
Number of hours of lecturers of reference
40
CFU 6
‌‌

Modalità esame

See the note.

Note modalità di esame

The exam could be a traditional oral one or, according to the student's choice,

be based on a research paper related to the topics touched during the course

Lecturer

View lecturer details

Prerequisiti

Basic knowledge of Measure Theory and Functional Analysis.


Programma

Part I: Variational problems with surface energies. Sets of finite perimeter, Sobolev spaces and BV functions. Compactness and lower semicontinuity in BV. SBV functions. Compactness and lower semicontinuity in SBV.


Part II: Plateau's and its weak formulation. Federer Fleming theory of currents, closure, compactness, boundary rectifiability.


Part III: Mean curvature motion. Level set formulation and Brakke's solutions. Existence of solutions via elliptic regularization.

Obiettivi formativi

The aim of the course is to present the basic concepts of Geometric Measure Theory. The course is organised according to specific goals, hence the tools and techniques will be introduced according to the goals.

Riferimenti bibliografici

L.Ambrosio, N.Fusco, D.Pallara: Functions of bounded variation and free discontinuity problems.


F.Maggi: Sets of finite perimeter and Geometric Variational problems.


P.Mattila: Geometry of sets and measures in Euclidean spaces.


F.Morgan: Geometric Measure Theory: a beginner's guide.


H.Federer: Geometric Measure Theory.

Go to the Advanced search