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

  • * Corresponding author: Connor Mooney

    * Corresponding author: Connor Mooney 

The first author is supported by NSF grant DMS-1854788

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  • 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.

    Mathematics Subject Classification: Primary: 53A10, 49Q20, 35B08.


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  • Figure 1.  The dilations of $ \Sigma_{kl} $ foliate one side of $ C_{kl} $

    Figure 2.  The solution curve is contained in the region $ R $ bounded by $ \Gamma_1, \, \Gamma_2 $ and $ \Gamma_3 $

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