MATS2110 Geometric Measure Theory (5 cr)

Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020

Description

Content

- Hausdorff measure and dimension, density theorems
- Mass distribution principle, Frostman's lemma, Riesz energies of measures
- Haar measures, uniformly distributed measures
- Projection theorems by Marstrand, Kaufman, and Mattila
- Fourier transforms of measures
- Rectifiable and purely unrectifiable sets
- Besicovitch's projection theorem

Learning outcomes

After the course the students know techniques to investigate geometric properties of general Borel sets and measures, and they are familiar with the notion and some properties of rectifiable sets in Euclidean spaces. The students will be provided with the necessary background to study advanced topics in modern geometric measure theory.

Description of prerequisites

Requires knowledge of basic theory of measure and integration, as covered in the courses

MATS111 Measure and Integration Theory 1
MATS112 Measure and Integration Theory 2

Study materials

P. Mattila: Geometry of Sets and Measures on Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press (1995)

Completion methods

Method 1

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Unpublished assessment item