English

If sufficient demand

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.

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.

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

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

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

Lectures

As a part of the examination, some lectures are given by the doctoral students.

Oral exam

Seminars given by participants

To pass, the doctoral student must give at least one lecture during the course.

Failed, pass

Knowledge in measure theory equivalent to a course in measure and integration theory.

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

FMA100F

 -04-22

FN1/Anders Gustafsson