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.

中文翻译：

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叶理证明劳森锥是 $ A_{\Phi} $-最小化

我们通过叶理证明 $ \mathbb{S}^k \times \mathbb{S}^l $ 上的锥体使每个 $ k, \, l \geq 1 $ 的参数椭圆泛函最小化。我们还分析了叶面中叶子在无穷远处的行为。这种分析激发了与此类泛函研究中出现的最小表面类型方程的非线性完整解的存在性和增长率相关的猜想。