Affiliation:
1. Department of Mathematics , University of Toronto , 40 St George Street , Toronto , ON M5S 2E4 , Canada
Abstract
Abstract
Some worrisome potential singularity models for the mean curvature flow are rotating ancient flows, i.e. ancient flows whose tangent flow at
-
∞
{-\infty}
is a cylinder
ℝ
k
×
S
n
-
k
{\mathbb{R}^{k}\times S^{n-k}}
and that are rotating within the
ℝ
k
{\mathbb{R}^{k}}
-factor. We note that while the
ℝ
k
{\mathbb{R}^{k}}
-factor, i.e. the axis of the cylinder, is unique by the fundamental work of Colding-Minicozzi, the uniqueness of tangent flows by itself does not provide any information about rotations within the
ℝ
k
{\mathbb{R}^{k}}
-factor. In the present paper, we rule out rotating ancient flows among all ancient noncollapsed flows in
ℝ
4
{\mathbb{R}^{4}}
.
Subject
Applied Mathematics,General Mathematics
Reference27 articles.
1. B. Andrews,
Noncollapsing in mean-convex mean curvature flow,
Geom. Topol. 16 (2012), no. 3, 1413–1418.
2. S. Brendle and K. Choi,
Uniqueness of convex ancient solutions to mean curvature flow in
ℝ
3
{\mathbb{R}^{3}}
,
Invent. Math. 217 (2019), no. 1, 35–76.
3. S. Brendle and K. Choi,
Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions,
Geom. Topol. 25 (2021), no. 5, 2195–2234.
4. O. Chodosh, K. Choi, C. Mantoulidis and F. Schulze,
Mean curvature flow with generic initial data,
preprint (2020), https://arxiv.org/abs/2003.14344.
5. B. Choi, P. Daskalopoulos, W. Du, R. Haslhofer and N. Sesum,
Classification of bubble-sheet ovals in
ℝ
4
{\mathbb{R}^{4}}
,
preprint (2022), https://arxiv.org/abs/2209.04931.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献