### MA 383: Introduction to Minimal Surfaces

#### Credits: 3:0

• Serre-Frenet formula for curves, Parametric surfaces, Isothermal parameters,
• Gauss Map, Gaussian Curvature, Mean curvature, Area functional etc.

• Surfaces that locally minimise area in Euclidean space (minimal surfaces).
• 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.

• Conjugate minimal surfaces. One parameter family of isometric minimal surfaces. the Bjorling problem and Schwartz’s solution to it.

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 maximal surfaces.

• Connection betwen minimal and maximal surfaces and Born Infeld solitions.
• Constant mean curvature surfaces of non-zero mean curvature (the optimization problem they solve)

#### Suggested books :

1. Dierkes, Hildebrandt, Kuster, Wohlrab, Minimal Surfaces I .
2. Manfredo Do Carmo, Differential Geometry of curves and surfaces .
3. Robert Osserman, A survey of minimal surfaces .
4. Yi Fang, Lectures on Minimal Surfaces in $R^n$ .
5. K. Kenmotsu, Surfaces of constant mean curvature .

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2625
E-mail: chairman.math[at]iisc[dot]ac[dot]in