PreprintarXiv licencearXiv
Degenerate neckpinches at the first N singular times
Abstract
For every integer N≥1, we construct a smooth closed connected strictly mean-convex rotationally symmetric surface in ℝ3 whose level set flow remains connected until extinction and has exactly one singular point at each of its first N singular times. These singularities are degenerate neckpinches with the Angenent--Velázquez asymptotics: the leading deviation from the cylinder under parabolic rescaling is a cubic Hermite term.
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BibTeX
@misc{chen2026degenerate,
title = {{Degenerate neckpinches at the first $N$ singular times}},
author = {Jingwen Chen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01419},
eprint = {2611.01419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01419},
}
RIS
TY - UNPB
TI - Degenerate neckpinches at the first N singular times
AU - Jingwen Chen
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01419
UR - https://arxiv.org/abs/2611.01419
AB - For every integer N≥1, we construct a smooth closed connected strictly mean-convex rotationally symmetric surface in ℝ^3 whose level set flow remains connected until extinction and has exactly one singular point at each of its first N singular times. These singularities are degenerate neckpinches with the Angenent--Velázquez asymptotics: the leading deviation from the cylinder under parabolic rescaling is a cubic Hermite term.
ER -