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Examples of topological sphere λ-self-expander
Abstract
A λ-self-expander F: Mn→ ℝn+1 is the solution of the isoperimetric problem of weight e|x|2/4. In this paper, for sufficiently large λ, we construct an immersed non-embedded spherical λ-self-expander in ℝn+1 with the mean curvature H>0. Moreover, we obtain the explicit solution for n=2.
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BibTeX
@misc{qi2026examples,
title = {{Examples of topological sphere $λ$-self-expander}},
author = {Mengdan Qi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10634},
eprint = {2610.10634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10634},
}
RIS
TY - UNPB
TI - Examples of topological sphere λ-self-expander
AU - Mengdan Qi
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.10634
UR - https://arxiv.org/abs/2610.10634
AB - A λ-self-expander F: M^n→ ℝ^n+1 is the solution of the isoperimetric problem of weight e^|x|^2/4. In this paper, for sufficiently large λ, we construct an immersed non-embedded spherical λ-self-expander in ℝ^n+1 with the mean curvature H>0. Moreover, we obtain the explicit solution for n=2.
ER -