发表机构
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于 Laplacian 代数的代数机制，通过闭包恒等式和代数不等式构造极小超锥体并判定其面积极小性、严格稳定性，应用于等参超锥体及复行列式实部零集，并给出奇次刚性与回拉判据。
AI 中文摘要
我们发展了一种基于 Laplacian 代数的代数机制，用于构造极小超锥体并确定其变分性质。相同的闭包恒等式可识别极小零集，并将子校准构造和定量散度估计归结为代数不等式。结合比较定理和 Jacobi 恒等式，所得的证书给出了面积极小性、严格面积极小性和严格稳定性的判据，允许非孤立奇点。应用包括面积极小的等参超锥体的多项式子校准、FKM 分裂四次族和 Clifford 三次族内的极小性分类，以及所有阶数至少为二的复行列式实部零集的严格面积极小性。我们还建立了梯度平方闭包下的奇次刚性以及子校准的回拉判据。代数恒等式和证书由可复现的精确符号计算支持。
英文摘要
We develop an algebraic mechanism based on Laplacian algebras for constructing minimal hypercones and determining their variational properties. The same closure identities identify minimal zero sets and reduce subcalibration construction and quantitative divergence estimates to algebraic inequalities. Combined with comparison theorems and Jacobi identities, the resulting certificates give criteria for area minimization, strict area minimization, and strict stability, allowing nonisolated singularities. Applications include polynomial subcalibrations for area-minimizing isoparametric hypercones, minimizing classifications within the FKM splitting quartic and Clifford cubic families, and strict area minimization for the zero sets of the real parts of complex determinants of every order at least two. We also establish odd-degree rigidity under gradient-square closure and a pullback criterion for subcalibrations. The algebraic identities and certificates are supported by reproducible exact symbolic computations.
