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Abstract: The radial projection from the unit ball into the Euclidean sphere is a well-known example of a harmonic map. In 2022 Nakauchi presented a generalization of this map based on an explicit recursive algorithm. In this talk we will first explain the mathematical structure behind the algorithm of Nakauchi and how one can systematically construct generalizations of the radial projection. It turns out that the generalized radial projection of Nakauchi is a critical point of the energy, p-energy as well as the extrinsic r-energy and we will study its stability with respect to the above mentioned functionals.