Valid from: Spring 2013
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-04-22
Course type: Third-cycle course
Teaching language: English
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.
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.
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.
L. C. Evans, R. F. Gariepy: Measure Theory and Fine Properties of Functions. CRC Press, 1992. ISBN 0849371570.
Type of instruction: Lectures. As a part of the examination, some lectures are given by the doctoral students.
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
Assumed prior knowledge: Knowledge in measure theory equivalent to a course in measure and integration theory.