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Analysis Seminar

Thursday, April 25, 2019 - 3:00pm to 4:00pm

Antonio de Rosa



University of Pennsylvania


We present our extension of Allard's celebrated rectifiability theorem to
the setting of varifolds with locally bounded anisotropic first variation.
We identify a necessary and sufficient condition on the integrand for its
validity and we discuss the connections of this condition to Almgren's
ellipticity. We apply this result to the set-theoretic anisotropic Plateau
problem, obtaining solutions to three different formulations: one
introduced by Reifenberg, one proposed by Harrison and Pugh and another
one studied by David. Moreover, we apply the rectifiability theorem to
prove an anisotropic counterpart of Allard's compactness result for
integral varifolds.
Some of the presented theorems are joint works with De Lellis, De
Philippis, Ghiraldin and Kolasiński.