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In this seminar, we focus on the minimal immersions of the 2-dimensional sphere in a space of constant sectional curvature. We will present some results and their proofs following the resources:  

References:

1. Chern, Shiing Shen - On the minimal immersions of the two-sphere in a space of constant curvature. Problems in analysis (Lectures at the Sympos. in honor of Salomon Bochner, Princeton Univ., Princeton, N.J., 1969), pp. 27–40. Princeton Univ. Press, Princeton, N.J., 1970.
2. Calabi, Eugenio - Minimal immersions of surfaces in Euclidean spheres. J. Differential Geometry 1 (1967), 111–125.