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: mean curvature, first and variation of area, parametric and non-parametric minimal surfaces, Bernstein's theorem, Weierstrass representation, examples, Plateau's problem, the Plateau Douglas problem, global minimal surfaces, etc. 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 is helpful but not a prerequisite.
- Enseignant·e: Stefan Wenger