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The singular set of minimal hypersurfaces with second fundamental form in L²

  • Reiner Schätzle (ETH Zürich, Departement der Mathematik)
A3 02 (Lab)

Abstract

We consider smooth, embedded, minimal $n$-hypersurfaces $M_j$ converging to a stationary varifold $\Sigma$. Under the assumption that the second fundamental $A_{M_j}$ of $M_j$ is bounded in $L^2$, that is $$\int^{2}_{M_j | \Lambda_{M_j} } d H^n \leq \Lambda_0 , $$ we prove that the Hausdorff dimension of the singular set is estimated by $$dim_H sing Sigma leq n-2$$