Regularity and structure of area minimizing currents mod p
speaker: Camillo De Lellis (Institute for Advanced Study, Princeton)abstract: Consider the interior singular set S of an area minimizing m-dimensional current T mod p in codimension n. In the 80es White showed that, when p is odd and n=1, S has dimension at most m−1. Prior to his work, a similar dimension bound was only known for p=3, m=2 and n=1 (Taylor) and for p=2 (from Federer's seminal paper it follows that S has dimension at most m-2). In a joint work with Hirsch, Marchese and Stuvard, we prove that the singular set S has dimension at most m−1 for every p,m and n. Our proof is based on a suitable modification of Almgren's regularity theory. Combining it with the results of Naber and Valtorta, for $p$ odd we are able to improve the dimension bound to rectifiability and finite (m-1)-dimensional measure. As a corollary we achieve the following structure theorem: for $p$ odd area-minimizing currents mod p can be decomposed into integral area-minimizing currents which meet at a common boundary.
timetable:
Mon 14 Jan, 15:00 - 16:00, Aula Magna Bruno Pontecorvo
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