Minimal Products via Weighted Spheres
Abstract
We establish an exact composition principle for spherical immersions coupled through coefficient profiles and norm-preserving bilinear maps. Under explicit mixed orthogonality, the spherical mean curvature vector splits into orthogonal input and profile contributions. The composition is minimal if and only if every input is minimal and the profile is W-minimal for the induced monomial weight. Tensor iteration allows weighted profiles to serve as inputs in further compositions. At fixed weights, Hsiang--Lawson reduction and Kapouleas--McGrath doubling yield closed embedded W-minimal profiles. When the effective exponents tend to infinity in positive limiting proportions, Gaussian transfer produces interior coefficient profiles from closed embedded self-shrinkers that are nondegenerate modulo rotations. The number of distinct corresponding profiles is bounded below by the Lusternik--Schnirelmann category of the rotation orbit.
Related
- Rigidity of Minimal Submanifolds in Spheres of Higher Codimension
- Curvature pinching for minimal Tangent-Yang-Mills hypersurfaces in spheres
- Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature
- A Curvature Gap for Minimal Submanifolds in Spheres
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BibTeX
@misc{zhang2026minimal,
title = {{Minimal Products via Weighted Spheres}},
author = {Yongsheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.24886},
eprint = {2609.24886},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24886},
}
RIS
TY - UNPB
TI - Minimal Products via Weighted Spheres
AU - Yongsheng Zhang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2609.24886
UR - https://arxiv.org/abs/2609.24886
AB - We establish an exact composition principle for spherical immersions coupled through coefficient profiles and norm-preserving bilinear maps. Under explicit mixed orthogonality, the spherical mean curvature vector splits into orthogonal input and profile contributions. The composition is minimal if and only if every input is minimal and the profile is W-minimal for the induced monomial weight. Tensor iteration allows weighted profiles to serve as inputs in further compositions. At fixed weights, Hsiang--Lawson reduction and Kapouleas--McGrath doubling yield closed embedded W-minimal profiles. When the effective exponents tend to infinity in positive limiting proportions, Gaussian transfer produces interior coefficient profiles from closed embedded self-shrinkers that are nondegenerate modulo rotations. The number of distinct corresponding profiles is bounded below by the Lusternik--Schnirelmann category of the rotation orbit.
ER -