PreprintarXiv licencearXiv
Counterexamples to preservation of flat normal bundles under mean curvature flow
Abstract
We construct an embedded torus and an entire graph in ℝ4 whose normal bundles are initially flat but lose this property instantaneously under mean curvature flow. We also give an example showing that the parallel principal normal condition is not preserved under mean curvature flow, even though the normal bundle remains flat along the flow.
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BibTeX
@misc{kunikawa2026counterexamples,
title = {{Counterexamples to preservation of flat normal bundles under mean curvature flow}},
author = {Keita Kunikawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.34291},
eprint = {2609.34291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34291},
}
RIS
TY - UNPB
TI - Counterexamples to preservation of flat normal bundles under mean curvature flow
AU - Keita Kunikawa
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.34291
UR - https://arxiv.org/abs/2609.34291
AB - We construct an embedded torus and an entire graph in ℝ^4 whose normal bundles are initially flat but lose this property instantaneously under mean curvature flow. We also give an example showing that the parallel principal normal condition is not preserved under mean curvature flow, even though the normal bundle remains flat along the flow.
ER -