Course Contents
With varying focus: Optimal surfaces in geometry, such as minimal surfaces (minima of surface area), Willmore surfaces (minima of bending energy), or problems under constraints, for instance surfaces of constant mean curvature; Representation of these surfaces as critical points of variational integrals as well as partial differential equations;Examples and existence statements, as well as properties of these surfaces, such as maximum principles.
Literature
references provided in the lecture; examples include:
Dierkes, Hildebrandt, Sauvigny: Minimal surfaces (Springer)
Kenmotsu: Surfaces of constant mean curvature (AMS)
Colding, Minicozzi: A course in minimal surfaces (AMS 2011)
Preconditions
recommended: Differential geometry
Online Offerings
moodle
With varying focus: Optimal surfaces in geometry, such as minimal surfaces (minima of surface area), Willmore surfaces (minima of bending energy), or problems under constraints, for instance surfaces of constant mean curvature; Representation of these surfaces as critical points of variational integrals as well as partial differential equations;Examples and existence statements, as well as properties of these surfaces, such as maximum principles.
Literature
references provided in the lecture; examples include:
Dierkes, Hildebrandt, Sauvigny: Minimal surfaces (Springer)
Kenmotsu: Surfaces of constant mean curvature (AMS)
Colding, Minicozzi: A course in minimal surfaces (AMS 2011)
Preconditions
recommended: Differential geometry
Online Offerings
moodle
- Lehrende: Karsten Große-Brauckmann
Semester: Inverno 2023/24