Geometric measure theory in metric spaces, spring 2010

Lecturer

Pertti Mattila

Scope

10 cu.

Type

Advanced studies

Prerequisites

Good background in measure and integration and real analysis, courses mitta ja integraali and reaalianalyysi I and II suffice

Lectures

Weeks 3-9 and 11-18 Tuesdays 10-12 and Thursdays 10-12 C123

No lectures and exercises on March 4, 9 and 11

Possible topics

• Hausdorff measures in metric spaces; Frostman's lemma and existence of subsets of finite and positive measure
• Lipschitz mappings into metric spaces and their 'Kirchheim-differentiability'
• rectifiable sets in the sense of Ambrosio and Kirchheim
• currents in the sense of Ambrosio and Kirchheim
• functions of bounded variation
• geometric measure theory in Heisenberg groups

Bibliography

K.J. Falconer, Geometry of fractal sets, Cambridge University Press, 1985
H.Federer, Geometric measure theory, Springer-Verlag, 1969
P. Mattila, Geometry of sets and measures in euclidean spaces, Cambridge University Press,1995
C.A. Rogers, Hausdorff measures, Cambridge University Press, 1970

Exercise group