Stationary and stable varifolds with singularities

Camillo De Lellis; Jonas Hirsch; Luca Spolaor

Stationary and stable varifolds with singularities

Differential Geometry 2026-04-14 v2 Analysis of PDEs

Authors: Camillo De Lellis , Jonas Hirsch , Luca Spolaor

Abstract

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

Keywords

isometric immersions singularity theory minimal surfaces

Cite

@article{arxiv.2509.21508,
  title  = {Stationary and stable varifolds with singularities},
  author = {Camillo De Lellis and Jonas Hirsch and Luca Spolaor},
  journal= {arXiv preprint arXiv:2509.21508},
  year   = {2026}
}

Comments

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

Stationary and stable varifolds with singularities

Abstract

Keywords

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