PreprintCC BY 4.0arXiv
Stationary varifolds with singularities II
Abstract
For every dimension m≥ 3, we show the existence of an open set U⊂ ℝm+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∖ {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 Cm−1, α regularity for g. That previous attempt contained an important error, which has been overcome using a crucial suggestion of gpt-astra-6.
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BibTeX
@misc{lellis2026stationary,
title = {{Stationary varifolds with singularities II}},
author = {Camillo De Lellis and Jonas Hirsch and Zachary Lihn and Luca Spolaor},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20647},
eprint = {2609.20647},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20647},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stationary varifolds with singularities II
AU - Camillo De Lellis
AU - Jonas Hirsch
AU - Zachary Lihn
AU - Luca Spolaor
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20647
UR - https://arxiv.org/abs/2609.20647
AB - For every dimension m≥ 3, we show the existence of an open set U⊂ 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∖ {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.
ER -