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.)