A proof by foliation that Lawson's cones are $A_{\Phi}$-minimizing

Connor Mooney; Yang Yang

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arXiv · 2102.07903

A proof by foliation that Lawson's cones are $A_{\Phi}$-minimizing

Connor Mooney·Yang Yang

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Abstract

We give a proof by foliation that the cones over $\mathbb{S}^k \times \mathbb{S}^l$ minimize parametric elliptic functionals for each $k,\,l \geq 1$. 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.

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Connor Mooney, Yang Yang. 2021-02-16. A proof by foliation that Lawson's cones are $A_{\Phi}$-minimizing. https://arxiv.org/abs/2102.07903

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