PreprintCC BY 4.0arXiv
The Brakke-BV structure of flat flows
Abstract
We show that, in ambient dimension at most seven, varifold limits of the minimizing movements scheme introduced by Almgren--Taylor--Wang and Luckhaus--Sturzenhecker are integral Brakke flows. As a consequence, we show that L1-limit points of the scheme, usually known as flat flows, are generalized BV flows. The result is unconditional and, in particular, remains valid even in the absence of energy convergence and in the presence of fattening.
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BibTeX
@misc{gennaro2026brakkebv,
title = {{The Brakke-BV structure of flat flows}},
author = {Daniele De Gennaro and Salvatore Stuvard},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15511},
eprint = {2610.15511},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15511},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Brakke-BV structure of flat flows
AU - Daniele De Gennaro
AU - Salvatore Stuvard
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15511
UR - https://arxiv.org/abs/2610.15511
AB - We show that, in ambient dimension at most seven, varifold limits of the minimizing movements scheme introduced by Almgren--Taylor--Wang and Luckhaus--Sturzenhecker are integral Brakke flows. As a consequence, we show that L^1-limit points of the scheme, usually known as flat flows, are generalized BV flows. The result is unconditional and, in particular, remains valid even in the absence of energy convergence and in the presence of fattening.
ER -