Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

401-4115-00L  Introduction to Geometric Measure Theory

SemesterAutumn Semester 2018
LecturersU. Lang
Periodicitynon-recurring course
Language of instructionEnglish


AbstractIntroduction to Geometric Measure Theory from a metric viewpoint. Contents: Lipschitz maps, differentiability, area and coarea formula, rectifiable sets, introduction to the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, normal currents, relation to BV functions, slicing, compactness theorem for integral currents and applications.
Objective
ContentExtendability and differentiability of Lipschitz maps, metric differentiability, rectifiable sets, approximate tangent spaces, area and coarea formula, brief survey of the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, currents with finite mass and normal currents, relation to BV functions, rectifiable and integral currents, slicing, compactness theorem for integral currents and applications.
Literature- Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces, 1995
- Herbert Federer, Geometric Measure Theory, 1969
- Leon Simon, Introduction to Geometric Measure Theory, 2014, web.stanford.edu/class/math285/ts-gmt.pdf
- Luigi Ambrosio and Bernd Kirchheim, Currents in metric spaces, Acta math. 185 (2000), 1-80
- Urs Lang, Local currents in metric spaces, J. Geom. Anal. 21 (2011), 683-742