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401-4115-00L 7 Credits BSC , DR , MSC D-MATH

Introduction to Geometric Measure Theory

Lecturers & Examiners: Prof. Dr. Urs Lang

VVZ CR n/a

Last Updated: 2026-06-03 00:07:40

Abstract

Introduction 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.

Content

Extendability 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.

Resources

Literature

- Lawrence C. Evans and Ronald F. Gariepy, Measure Theory and Fine Properties of Functions, 1992 - Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces, 1995 - Urs Lang, Notes on Rectifiability, https://people.math.ethz.ch/~lang/rect_notes.pdf - Herbert Federer, Geometric Measure Theory, 1969 - Steven Krantz and Harold R. Parks, Geometric Integration Theory, 2008 - 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

General Information

Language: English
Levels: BSC , DR , MSC

Examination

Type: session examination
Mode: oral 20 minutes

Prüfungssprache: Deutsch oder Englisch / Language of examination: English or German

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Introduction to Geometric Measure Theory	No time listed	4 h weekly

Offered In

Mathematics Bachelor
- Core Courses and Elective Courses
  - Electives
    - Selection: Analysis
Mathematics Master
- Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  - Electives: Pure Mathematics
    - Selection: Analysis
Doctorate Mathematics (More Information at: )
- Subject Specialisation (The list of courses eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
  - Graduate School (Official website of the Zurich Graduate School in Mathematics: )