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).

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%)

Credit Score: 4