Geometric measure theory is the study of geometric objects with the tools of measure theory. It occupies a central place in modern Geometric Analysis, where it has led to the resolution of many conjectures such as Plateau's problem and intriguing questions about soap bubbles. It is also extremely useful as a toolkit of methods that have enabled many new discoveries in other fields of Mathematics, spanning from Mathematical Material Science, over the Theory of PDEs and the Calculus of Variations, all the way to Number Theory. This course will give an introduction to this important area.
- Motivation: Plateau's Problem
- Hausdorff Measures
- Area & Coarea Formula
- Forms and Stokes' Theorem
- Integral Currents
- Deformation Theorem
- Resolution of Plateau's Problem
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