多模块极小乘积：精确复合、闭型面与高斯传递
Multi-Module Minimal Products: Exact Composition, Closed Profiles, and Gaussian Transfer
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中文总结 AI 辅助
本文为球面浸入的复合建立精确极小性判据，并构造闭嵌入的W-极小型面，通过高斯传递从非退化种子生成内部型面。
中文摘要 AI 辅助
我们为通过系数型面和保范双线性映射耦合的球面浸入建立了精确的复合原理。在显式的混合正交性条件下，球面平均曲率向量分解为正交的输入贡献和型面贡献。当且仅当每个输入都是极小的且型面对显式的单项式权是$W$-极小的，该复合才是极小的。利用Hsiang--Lawson约化和Kapouleas--McGrath粘合，我们构造了闭嵌入的$W$-极小型面，包括具有无界中间Betti数的族。对于足够大的可比较输入维数，本文发展的高斯传递从闭嵌入且模旋转非退化的高斯种子产生内部型面。
英文摘要
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.
