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

Abstract

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.