Geometric Measure Theory I

Geometric Measure Theory I

Semester
WiSe 2024 / 25

Lecturer
Tim Laux

Type of course (Veranstaltungsart)
Vorlesung

German title
Geometrische Maßtheorie I

Contents
In the graduate-level course Geometric Measure Theory 1 we will study sets of finite perimeter which
appear in many geometric problems as they generalize in a natural measure theoretic way the notion
of sets with smooth boundaries and enjoy excellent compactness properties. After paving our way
to defining sets of finite perimeter, we will study their compactness, structure, and regularity
properties. If time permits, we will discuss further topics like minimal clusters, free
discontinuity problems, and some applications.

Literature
Maggi, Francesco. Sets of finite perimeter and geometric variational problems: an introduction to
Geometric Measure Theory. No. 135. Cambridge University Press, 2012. L. Craig Evans and Ronald F.
Gariepy. Measure theory and fine properties of functions. Chapman and Hall/CRC, 2015. Luigi
Ambrosio, Nicola Fusco, and Diego Pallara. Functions of bounded variation and free discontinuity
problems. Vol. 254. Oxford: Clarendon Press, 2000.

Recommended previous knowledge
Working knowledge in measure theory and analysis is assumed. (The basic training in analysis is
sufficient; Functional Analysis is useful but not necessary.)

Time/Date
Th, Fr: 8:15-10:00

Location
M104

Registration

Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: einmal zufriedenstellend vorrechnen

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: individual appointments, re-exam: Date:

Modules
BV, MV, MGAGeo, MAngAn

ECTS
9