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

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

paper · pdf · doi:10.48550/arxiv.2102.07903

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

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