PreprintCC0arXiv
The double sphere solution in the liquid drop model
Abstract
We consider the problem of finding critical domains Ω⊂ℝ3 for the energy functional ℰ (Ω) = Per (Ω) + 1/2 iintΩ× Ω (dx dy)/(|x−y|) under the volume constraint |Ω|=V. We look for smooth, embedded, compact surfaces ∂Ω that solve this problem. We construct an axially symmetric, non-minimizing solution that, for a sufficiently small V>0, resembles the union of two balls with volume V/2 connected by a tiny, approximately catenoidal neck with a width of the order V4/3.
Related
- On the existence of minimizers for the generalized liquid drop model
- Some remarks on nonexistence in the Gamow liquid drop model
- Symmetry breaking in the liquid drop model with screened interactions
- An exact Delaunay flux identity for compact equilibria in the liquid drop model
- Failure of dimension drop for harmonic measure on Ahlfors regular flat boundaries
BibTeX
@misc{pino2026double,
title = {{The double sphere solution in the liquid drop model}},
author = {Manuel del Pino and Rupert L. Frank and Monica Musso},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00108},
eprint = {2609.00108},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00108},
note = {CC0},
}
RIS
TY - UNPB
TI - The double sphere solution in the liquid drop model
AU - Manuel del Pino
AU - Rupert L. Frank
AU - Monica Musso
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.00108
UR - https://arxiv.org/abs/2609.00108
AB - We consider the problem of finding critical domains Ω⊂ℝ^3 for the energy functional ℰ (Ω) = Per (Ω) + 1/2 iint_Ω× Ω (dx dy)/(|x−y|) under the volume constraint |Ω|=V. We look for smooth, embedded, compact surfaces ∂Ω that solve this problem. We construct an axially symmetric, non-minimizing solution that, for a sufficiently small V>0, resembles the union of two balls with volume V/2 connected by a tiny, approximately catenoidal neck with a width of the order V^4/3.
ER -