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401-4115-DRL 2 Credits DR D-MATH

Introduction to Geometric Measure Theory

Lecturers & Examiners: Prof. Dr. Urs Lang
Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to with their name, course number and student ID. Please see
VVZ CR n/a

Last Updated: 2026-02-05 16:14:50

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
DR

Examination

Type
ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Introduction to Geometric Measure Theory
  • Tue 09:15-10:00 (HG D 5.2)
  • Thu 10:15-12:00 (LFW B 1)
3 h weekly

Offered In