Boundary Plateau Laws I

We give a complete list of the possible local shapes of soap films where they wet the whole wire. In rigorous terms, given a straight line $\ell \subset \mathbb R^3$, we study $2$-dimensional cones in $\mathbb R^3$ which contain $\ell$ and are Almgren minimizing with respect to $\ell$.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.37559
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

Boundary Plateau Laws I

Federico Glaudo, Camillo De Lellis
arXiv (Cornell University)
Geometric Analysis and Curvature Flows
preprint

Boundary Plateau Laws I

Federico Glaudo, Camillo De Lellis
preprint en

Abstract

We give a complete list of the possible local shapes of soap films where they wet the whole wire. In rigorous terms, given a straight line $\ell \subset \mathbb R^3$, we study $2$-dimensional cones in $\mathbb R^3$ which contain $\ell$ and are Almgren minimizing with respect to $\ell$.

arXiv (Cornell University)
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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Boundary Plateau Laws I — Federico Glaudo, Camillo De Lellis · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS