**First Meeting: **11 August 2023

**Class Timings: **Wednesdays 4:30 - 5:30 PM and Fridays 3:00 - 5:00 PM

**Course Description:** It will include basics of minimal and maximal surfaces, and other extremal surfaces.

1. Differential geometry of curves and surfaces.

2. Introdiuction to minimal surfaces -- definition (mean curvature zero), area minimizing property, Weierstrass-Enneper representation of minimal surfaces, Bjorling problem

3. Introduction to maximal surface- Lorentz-Minkowski space, mean curvature zero surfaces, maximizer of "energy" functional, Weierstrass-Enneper represenation of maximal surfaces, Bjorling problem

4. Introduction to Constant Mean curvature surfaces -- definition and energy minimizing property with constraints.

5. Introduction to petal growth (if time permits).

**References:**

1. Do Carmo: Differential Geometry of Curves and Surfaces (topic 1)

2. R. Osserman: Survey of Minimal Surfaces (topic 2)

3. Dierkes, Hildebrandt et al: Lectures on Minimal surfaces (topic 2)

4. R. Lopez: Differential geometry of curves and surfaces in Lorentz-Minkowski space (topic 3)

5. K. Kenmotsu: Surfaces with Constant Mean Curvature (topic 34)

6. L. Mahadevan et. al --papers. (topic 5)

**Course Outcome:**In this course the students will get familiarity with surfaces which extremize energy functionals in Euclidean and Lorentz-Minkowski 3-d space. They will get to see the most general solutions locally.

**Course Evaluation:**Assignments (10%) and Presentations (90%)

- Teacher: Rukmini Dey

Credit Score: 4