Stationary and stable varifolds with singularities

Abstract

We construct minimal $m$-dimensional immersions in ${\mathbb{R}}^{m+1}$, equipped with a $C^{1,\hat{I}\pm }$ metric, $\hat{I}\pm \in [0,1)$, with a sequence of \emph{catenoidal necks} or \emph{floating disks} converging to an isolated, multiplicity $2$, singular flat point.

G. Orriols pointed out an important mistake in the original version. As a result the regularity of the ambient manifold in our construction does not improve with the dimension