The minimal cones C = \{ (x, y) ∈ Rᵐ × Rᵐ; |x| ≤ |y| \} are shown to minimize the weighted perimeter Pα (E) = ∫ |x|α |D φE| , α ∈ R , E ⊂ Rᵐ × Rᵐ , whenever m + α ≥ 4 . This completes recent results of Dierkes and Huisken [Math. Ann. (2023)].
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Ulrich Dierkes (2024) studied this question.
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