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In this learning seminar series, we will give an introduction to minimal submanifolds of the higher dimensional spheres. In particular we give estimates on the index of the Jacobi operator. Talk about applications on the Plateau's problem and Bernstein conjecture. 

The topic of this week is: 

    "Laplacian of the Shape Operator"

We will be following the classical beautiful paper.

References:

1. Simons, James - Minimal varieties in riemannian manifolds. Ann. of Math. (2) 88 (1968), 62–105.