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arXiv · 2609.24886

Multi-Module Minimal Products: Exact Composition, Closed Profiles, and Gaussian Transfer

Yongsheng Zhang
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Abstract

We establish an exact composition principle for spherical immersions coupled through coefficient profiles and norm-preserving bilinear maps. Under an explicit mixed-orthogonality condition, 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 an explicit monomial weight. Using Hsiang--Lawson reduction and Kapouleas--McGrath gluing, we construct closed embedded $W$-minimal profiles, including families with unbounded intermediate Betti numbers. For sufficiently large comparable input dimensions, a Gaussian transfer developed in this paper produces interior profiles from closed embedded Gaussian seeds that are nondegenerate modulo rotations.

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Yongsheng Zhang. 2026-09-21. Multi-Module Minimal Products: Exact Composition, Closed Profiles, and Gaussian Transfer. https://arxiv.org/abs/2609.24886

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