Course Syllabus for

Geometric Measure Theory
Geometrisk m├ątteori

FMA100F, 15 credits

Valid from: Spring 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-04-22

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English

Aim

The course is established to give an overview of the basic results in geometric measure theory and the methods used therein, and to provide the doctoral student with knowledge and skills that are relevant for the student's own research.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must For a passing grade the doctoral student must be able to reproduce key results and scetch their proofs.

Competences and Skills

For a passing grade the doctoral student must For a passing grade the doctoral student must be able to apply the basic techniques, results and concepts to concrete examples and exercises.

Judgement and Approach

For a passing grade the doctoral student must For a passing grade the doctoral student must be able to compare and discuss key results.

Course Contents

Covering theorems, differentiation of measures and integrals, Hausdorff measures, the isodiametric inequality, Rademacher's theorem, the area and coarea formula, Sobolev spaces, Stokes' theorem, Currents.

Course Literature

L. C. Evans, R. F. Gariepy: Measure Theory and Fine Properties of Functions. CRC Press, 1992. ISBN 0849371570.

Instruction Details

Type of instruction: Lectures. As a part of the examination, some lectures are given by the doctoral students.

Examination Details

Examination formats: Oral exam, seminars given by participants. To pass, the doctoral student must give at least one lecture during the course.
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: Knowledge in measure theory equivalent to a course in measure and integration theory.

Course Occasion Information

Contact and Other Information

Course coordinators:


Complete view