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Sharp Sobolev inequalities on minimal immersions via optimal transport
We prove that, for $2\leq p<n$, the optimal $L^p$-Sobolev constant on every complete $n$-dimensional Euclidean minimal immersion without boundary is the Euclidean Aubin--Talenti constant. The proof combines optimal transport to a suitably chosen target with a two-kernel comparison linking the tangen
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