PreprintCC BY 4.0arXiv
On the Gage-Hamilton-Grayson Theorem for free boundary curves
Abstract
We provide an alternative and independent proof of the analogue of the Gage-Hamilton-Grayson Theorem for embedded free boundary curve shortening flows in a convex planar domain established by Langford-Zhu. Our proof is based on blowup arguments introduced by B. White in his work on mean-convex mean curvature flow.
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BibTeX
@misc{bao2026gagehamiltongrayson,
title = {{On the Gage-Hamilton-Grayson Theorem for free boundary curves}},
author = {Yueheng Bao and Lorenzo Sarnataro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09557},
eprint = {2610.09557},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09557},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Gage-Hamilton-Grayson Theorem for free boundary curves
AU - Yueheng Bao
AU - Lorenzo Sarnataro
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09557
UR - https://arxiv.org/abs/2610.09557
AB - We provide an alternative and independent proof of the analogue of the Gage-Hamilton-Grayson Theorem for embedded free boundary curve shortening flows in a convex planar domain established by Langford-Zhu. Our proof is based on blowup arguments introduced by B. White in his work on mean-convex mean curvature flow.
ER -