PreprintarXiv licencearXiv
Non-migration for planar elastic flows
Abstract
We consider a closed planar curve evolving by the free or the length-preserving elastic flow. We prove that the scale-invariant bound L∫ k2 ds≤ 4π2+8/3 at the initial time prevents the entire curve from crossing any line between two times. For the free flow, the proof combines a monotonicity estimate for the normalized bending energy with a barrier that compares centroid motion to an expanding energy radius. For the length-preserving flow, a quantitative gradient estimate controls the total centroid displacement.
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BibTeX
@misc{novaga2026nonmigration,
title = {{Non-migration for planar elastic flows}},
author = {Matteo Novaga},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07242},
eprint = {2611.07242},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07242},
}
RIS
TY - UNPB
TI - Non-migration for planar elastic flows
AU - Matteo Novaga
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07242
UR - https://arxiv.org/abs/2611.07242
AB - We consider a closed planar curve evolving by the free or the length-preserving elastic flow. We prove that the scale-invariant bound L∫ k^2 ds≤ 4π^2+8/3 at the initial time prevents the entire curve from crossing any line between two times. For the free flow, the proof combines a monotonicity estimate for the normalized bending energy with a barrier that compares centroid motion to an expanding energy radius. For the length-preserving flow, a quantitative gradient estimate controls the total centroid displacement.
ER -