ADVANCED ANALYSIS 3
Learning outcomes of the course unit
Illustrate some advance concepts of geometric measure theory and introduce the students to contemporary research topics.
Analysis courses of the first two years, topology of R^n, courses of "Spazi di funzioni" and "Teoria della misura e dell'integrazione".
Course contents summary
Geometric measure theory. Functions with bounded variation. Sets with finite perimeter and reduced boundary. Fine properties of functions with bounded variation. Regularity of the reduced boundary. Parametric minimal surfaces and almost everywhere regularity.
Luigi Ambrosio, Nicola Fusco and Diego Pallara, "Functions of bounded variation and free discontinuity problems", Oxford mathematical monographs, 2000. Lawrence C. Evans and Ronald F. Gariepy, "Measure theory and fine properties of functions", CRC press, 1992. Enrico Giusti, "Minimal surfaces and functions of bounded variation", Birkhauser, 1984.
Lessons. Oral examination, consisting of a seminar on a specific topic chosen by the teacher and the student and of a discussion of the main topics of the course.