{"ID":23646986,"CreatedAt":"2026-09-18T07:39:37.512926072Z","UpdatedAt":"2026-09-18T07:39:37.512926072Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20647","arxiv_id":"2609.20647","title":"Stationary varifolds with singularities II","abstract":"For every dimension $m\\geq 3$, we show the existence of an open set $U\\subset \\mathbb R^{m+1}$, a smooth Riemannian metric $g$ on it, and an integral $m$-dimensional stationary varifold $V$ in $(U,g)$ with the following properties. $V$ has a flat tangent plane of multiplicity $2$ at an interior point $p$, it is a smooth immersed minimal surface in $U\\setminus \\{p\\}$, and it has infinite topology in any neighborhood of $p$. The construction starts from an idea of three of the authors, who in \\cite{DHS} tried to build a similar example with $C^{m-1, α}$ regularity for $g$. That previous attempt contained an important error, which has been overcome using a crucial suggestion of gpt-astra-6.","short_abstract":"For every dimension $m\\geq 3$, we show the existence of an open set $U\\subset \\mathbb R^{m+1}$, a smooth Riemannian metric $g$ on it, and an integral $m$-dimensional stationary varifold $V$ in $(U,g)$ with the following properties. $V$ has a flat tangent plane of multiplicity $2$ at an interior point $p$, it is a smoot...","url_abs":"https://arxiv.org/abs/2609.20647","url_pdf":"https://arxiv.org/pdf/2609.20647v1","authors":"[\"Camillo De Lellis\",\"Jonas Hirsch\",\"Zachary Lihn\",\"Luca Spolaor\"]","published":"2026-09-17T16:26:42Z","proceeding":"math.DG","tasks":"[\"math.DG\",\"math.AP\"]","methods":"[]","has_code":false}