minimal_surfaces
Here is some useful material for the Minimal surfaces course I am currently teaching in Scuola Normale in Pisa.
More information here.
Lectures
| Date | Where | Topic |
|---|---|---|
| 20/10/2026 2pm | Aula Bianchi Scienze | Introduction and preliminaries in Riemannian geometry |
| 22/10/2026 4pm | Aula Mancini | Geodesics and first variation of the area |
| 27/10/2026 2pm | Aula Bianchi Scienze | First consequences of minimality and monotonicity formula |
| 29/10/2026 4pm | Aula Tonelli | Fáry-Milnor theorem, Hoffman-Meeks halfspace theorem, and Weierstrass representation |
| 03/11/2026 2pm | Aula Bianchi Scienze | Second variation of the area, Bernstein and stable Bernstein theorems |
| 04/11/2026 9am | Aula Mancini | Basic compactness theorem, curvature estimates for stable minimal hypersurfaces, index of minimal submanifold |
| 10/11/2026 2pm | Aula Bianchi Scienze | |
| 12/11/2026 4pm | Aula Mancini | |
| 13/11/2026 4pm | Aula Volterra | Exercise class and discussion |
| 17/11/2026 2pm | Aula Bianchi Scienze | |
| 19/11/2026 4pm | Aula Mancini | |
| 24/11/2026 2pm | Aula Marie Curie | |
| 26/11/2026 4pm | Aula Fermi | |
| 01/12/2026 2pm | Aula Bianchi Scienze | |
| 03/12/2026 4pm | Aula Mancini | |
| 08/12/2026 2pm | NO CLASS | |
| 10/12/2026 4pm | Aula Fermi | |
| 15/12/2026 2pm | Aula Bianchi Scienze | |
| 17/12/2026 4pm | Aula Russo |
Notes
These are work in progress notes of the course: Minimal surfaces notes. The transcription of the handwritten notes into LaTex is currently partially automated using a LLM and revised by Andrea Rocca.
Exercises
| Date | Exercises | Topic |
|---|---|---|
| 20/10/2026 | Exercise sheet 0 | Review of Riemannian geometry |
| 28/10/2026 | Exercise sheet 1 | Minimal surfaces in Euclidean space |
Literature and useful resources
- [CM11] T. Colding, W. Minicozzi, A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp.
- [Whi16] B. White, Introduction to minimal surface theory. Geometric analysis, 387-438, IAS/Park City Math. Ser., 22. American Mathematical Society, Providence, RI, 2016.
- [Cho25] O. Chodosh, Introduction to minimal surfaces. Notes from the course Math 286 given at Stanford.
- [Web26] M. Weber, Minimal surfaces repository. Online collection of minimal surfaces illustrations.