Geometric Measure Theory I

Period of duration of course
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Course info
Number of course hours
20
Number of hours of lecturers of reference
20
Number of hours of supplementary teaching
0
CFU 3
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Type of exam

Oral exam

Lecturer

View lecturer details

Prerequisites

Students of Laurea Magistrale, PhD students

Programme

Abstract measure theory
Weak convergence in L^p spaces
Measures in metric spaces
Outer measures and weak∗ convergence
Operations on measures
Convolution
Sobolev spaces
Lipschitz functions
Covering and derivation of measures
Disintegration
Functionals defined on measures
Tangent measures
Hausdorff measures
Rectifiable sets
Area formula
Approximate tangent space
Coarea formula
Minkowski content

Educational aims

The goal of the course is to provide basic mathematical tools for the study of measures and mildly regular sets in Euclidean spaces, from the geometric viewpoint. These tools are preliminary to the second part of the course, but they have an independent interest

Bibliographical references

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

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

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

H.Federer: Geometric Measure Theory