401-4115-00L  Introduction to Geometric Measure Theory

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



Courses

NumberTitleHoursLecturers
401-4115-00 VIntroduction to Geometric Measure Theory3 hrs
Tue09:15-10:00HG D 3.2 »
Thu10:15-12:00HG F 26.5 »
U. Lang

Catalogue data

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, Link
- 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

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits6 credits
ExaminersU. Lang
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
Additional information on mode of examinationPrüfungssprache: Deutsch oder Englisch / Language of examination: English or German
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

No public learning materials available.
Only public learning materials are listed.

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Mathematics BachelorSelection: AnalysisWInformation
Mathematics MasterSelection: AnalysisWInformation