PreprintCC BY 4.0arXiv
On the existence of minimizers for the generalized liquid drop model
Abstract
We consider a broad class of generalized liquid drop models in which a perimeter term competes with repulsive nonlocal interactions with finite first moments. For all such kernels satisfying the natural physical assumption of reflection positivity we show existence of minimizers for all masses, in the (super-)critical regime. Moreover, in the subcritical regime we give the first quantitative estimate of the range of masses for which existence holds, which converges to the whole positive real line as one approaches the critical regime. This result builds on the nonlocal curvature approach introduced and developed in the periodic setting in \cite{dr24}.
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BibTeX
@misc{cheng2026existence,
title = {{On the existence of minimizers for the generalized liquid drop model}},
author = {Xiaopeng Cheng and Sara Daneri and Eris Runa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40500},
eprint = {2610.40500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40500},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the existence of minimizers for the generalized liquid drop model
AU - Xiaopeng Cheng
AU - Sara Daneri
AU - Eris Runa
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40500
UR - https://arxiv.org/abs/2610.40500
AB - We consider a broad class of generalized liquid drop models in which a perimeter term competes with repulsive nonlocal interactions with finite first moments. For all such kernels satisfying the natural physical assumption of reflection positivity we show existence of minimizers for all masses, in the (super-)critical regime. Moreover, in the subcritical regime we give the first quantitative estimate of the range of masses for which existence holds, which converges to the whole positive real line as one approaches the critical regime. This result builds on the nonlocal curvature approach introduced and developed in the periodic setting in \cite{dr24}.
ER -