A proof by foliation that Lawson's cones are A_Φ-minimizing

2021/02/16 by Connor Mooney, Yang Yang, Mooney, Connor +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.2102.07903

To appear in Discrete Contin. Dyn. Syst

arxiv created 2021/04/02 · arxiv updated 2021/04/05

Abstract

We give a proof by foliation that the cones over \mathbbS^k × \mathbbS^l minimize parametric elliptic functionals for each k, l ≥ 1. We also analyze the behavior at infinity of the leaves in the foliations. This analysis motivates conjectures related to the existence and growth rates of nonlinear entire solutions to equations of minimal surface type that arise in the study of such functionals.

Citations

• Minimal Varieties in Riemannian Manifolds

Related

• Minimizing cones associated with isoparametric foliations
• Regularity of minimal surfaces near quadratic cones
• On FKM isoparametric hypersurfaces in \mathbbSⁿ × \mathbbSⁿ and new area-minimizing cones
• Minimal surfaces near Hardt-Simon foliations
• Stable solutions to some elliptic problems: minimal cones, the Allen-Cahn equation, and blow-up solutions