PreprintCC BY-NC-ND 4.0arXiv
The second gap for self-shrinkers with constant norm of the second fundamental form
Abstract
Let X: Mn→ ℝn+1 be a complete self-shrinker with constant squared norm of the second fundamental form S. In this paper, we prove that if S≤ 10/7, then S=1 or S=0, and the self-shrinker is isometric to either a round sphere 𝕊n(√n) with the center at the origin, or a cylinder 𝕊k(√k)× ℝn−k, 1≤ k≤ n−1, or a plane through the origin.
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BibTeX
@misc{cheng2026second,
title = {{The second gap for self-shrinkers with constant norm of the second fundamental form}},
author = {Pengpeng Cheng and Tongzhu Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30697},
eprint = {2609.30697},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30697},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The second gap for self-shrinkers with constant norm of the second fundamental form
AU - Pengpeng Cheng
AU - Tongzhu Li
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30697
UR - https://arxiv.org/abs/2609.30697
AB - Let X: M^n→ ℝ^n+1 be a complete self-shrinker with constant squared norm of the second fundamental form S. In this paper, we prove that if S≤ 10/7, then S=1 or S=0, and the self-shrinker is isometric to either a round sphere 𝕊^n(√n) with the center at the origin, or a cylinder 𝕊^k(√k)× ℝ^n−k, 1≤ k≤ n−1, or a plane through the origin.
ER -