PreprintCC BY 4.0arXiv
Foliation by bi-rotational self shrinkers in Euclidean space
Abstract
In this note, we prove that there exist two families of bi-rotational asymptotically conical self shrinkers with boundary called `trumpets', and two families of bi-rotational self shrinkers with boundary which close up called `disks', so that these families together with two generalized self shrinking cylinders, and a minimal cone foliate the whole space except some compact set containing the origin.
Related
- Rigidity theorems of complete self-shrinkers in the Euclidean space
- Rigidity of Immersed Gauss Curvature Shrinkers in Euclidean Space
- The global structure of bi-rotational self-shrinkers
- Complete self-shrinkers with constant norm of the second fundamental form in RR4
- Rigidity of Three-Dimensional Self-Shrinkers with Constant Norm of the Second Fundamental Form
BibTeX
@misc{park2026foliation,
title = {{Foliation by bi-rotational self shrinkers in Euclidean space}},
author = {Junyoung Park},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.11046},
eprint = {2608.11046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11046},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Foliation by bi-rotational self shrinkers in Euclidean space
AU - Junyoung Park
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2608.11046
UR - https://arxiv.org/abs/2608.11046
AB - In this note, we prove that there exist two families of bi-rotational asymptotically conical self shrinkers with boundary called `trumpets', and two families of bi-rotational self shrinkers with boundary which close up called `disks', so that these families together with two generalized self shrinking cylinders, and a minimal cone foliate the whole space except some compact set containing the origin.
ER -