Gauss Map, Gaussian Curvature, Mean curvature, Area functional etc.
Harmonic coordinates in isothermal parameters. Examples of minimal surfaces.
Minimal surfaces with boundary: Plateau’s problem.
The gauss map for minimal surfaces with some examples.
The Weierstrass-Enneper representation of minimal surfaces. Many more examples
of minimal surfaces.
If time permits:
Surfaces that locally maximise area in Lorenztian space (maximal surfaces). A
lot of examples and analogous results, as in minimal surface theory, for