A Generalized Lai–Wei Construction and New Families of Area-Minimizing Hypercones

Our results are twofold. Inspired by recent work on weighted spheres, we extend the Lai–Wei construction from one to several independent isoparametric inputs, replacing its profile curve by a hypersurface profile to generate minimal hypersurfaces in spheres. Using a curvature criterion, we obtain new infinite families of area-minimizing hypercones from the original construction and its extensions.