The study of minimal surfaces has attracted the attention of mathematicians since the 18th century and its problems stimulated the development
of many neighbouring domains of mathematics, notably complex analysis,
Partial Differential Equations, and Geometric Measure Theory.
The present course gives an introduction to the theory of minimal surfaces and covers classical as well as modern aspects. Topics include: first and second variation of area, parametric and non-parametric minimal surfaces, Bernstein's theorem and recent generalizations, Weierstrass representation, examples, Plateau's problem, branch points,
functions of bounded variation and existence and regularity of minimal hypersurfaces in higher dimensions.
The students will develop a good understanding of the basics of minimal surface theory, through examples and theory. They will learn about classical as well as recent results
and acquire the analytic background which allows them to solve problems
in the area. Prerequisites for the course are Analysis I - IV; familiarity with Riemannian Geometry and PDEs is helpful but not a prerequisite.
- Enseignant·e: Stefan Wenger
- Enseignant·e non éditeur: Damaris Meier