turkmath.org

In this seminar series, we will give an introduction to some topics in minimal submanifold theory. In particular minimal embeddings of spheres into higher dimensional spheres especially as holomorphic curves. Topics to be covered are as follows.

      "An application of the Riemann-Roch formula to the minimal surfaces"

We will be using the following resources.

References:

1. N. Ejiri - The Index of Minimal Immersions of S^2 into S^{2n}.
   Mathematische Zeitschrift. (1983).


2. Kühnel, Wolfgang - Differential geometry. Curves—surfaces—manifolds. Third edition.
   Translated from the 2013 German edition. American Mathematical Society. 2015.


3. J. Madnick - The Second Variation of Null-Torsion Holomorphic Curves in the 6-Sphere.
   ArXiv:2101.09580 (Jan 2021) 35 pages.


4. J. Madnick - Free-Boundary Problems for Holomorphic Curves in the 6-Sphere.
   Arxiv:2105.10562 (May 2021). 17 pages.


5. S. Montiel and F. Urbano - Second Variation of Superminimal Surfaces into Self-Dual Einstein 4-Manifolds. Trans. AMS. (1997).