Global Minimality and Rigidity of the Constraint Map Vortex
Bin Deng, Jiahuan Li, Yilu Liu, Xi-Nan Ma
Abstract
We consider the minimization problem \[ \∫B1|Du|2:\ u∈ W1,2(B1; Rn), u=x\ on ∂ B1, |u| a\, 0<a<1. \] Figalli, Guerra, Kim, and Shahgholian proved that the canonical radial vortex is the unique global minimizer for n7, and asked whether the same holds in dimensions \(3 n 6\). We answer this question affirmatively, thereby completing the global minimality and rigidity of the constraint map vortex in every dimension \(n3\).
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