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Existence of rotationally symmetric embedded f-minimal tori
Abstract
Let n≥2, and let f:[0,+∞)→ℝ be a smooth function satisfying f''≥0 and 0<m≤ f'≤ M for some constants m and M. We prove that ℝn+1, endowed with the conformal metric ds2=e−f(|x|2)/2n∑i=1n+1dxi2, admits a compact, embedded, rotationally symmetric minimal hypersurface diffeomorphic to S1× Sn−1. This extends Angenent's existence theorem for self-shrinking tori, which is recovered when f(s)=s.
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BibTeX
@misc{peng2026existence,
title = {{Existence of rotationally symmetric embedded f-minimal tori}},
author = {Peng Peng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.05022},
eprint = {2605.05022},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.05022},
}
RIS
TY - UNPB
TI - Existence of rotationally symmetric embedded f-minimal tori
AU - Peng Peng
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2605.05022
UR - https://arxiv.org/abs/2605.05022
AB - Let n≥2, and let f:[0,+∞)→ℝ be a smooth function satisfying f''≥0 and 0<m≤ f'≤ M for some constants m and M. We prove that ℝ^n+1, endowed with the conformal metric ds^2=e^−f(|x|^2)/2n∑_i=1^n+1dx_i^2, admits a compact, embedded, rotationally symmetric minimal hypersurface diffeomorphic to S^1× S^n−1. This extends Angenent's existence theorem for self-shrinking tori, which is recovered when f(s)=s.
ER -