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Center manifold: A case study

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  • Following Almgren's construction of the center manifold in his Big regularity paper, we show the $C^{3,\alpha}$ regularity of area-minimizing currents in the neighborhood of points of density one without using the nonparametric theory. This study is intended as a first step towards the understanding of Almgren's construction in its full generality.
    Mathematics Subject Classification: Primary: 49Q15, 49Q05; Secondary: 35D10.


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