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arXiv · 2608.24805

Global Minimality and Rigidity of the Constraint Map Vortex

Bin Deng·Jiahuan Li·Yilu Liu·Xi-Nan Ma
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Abstract

We consider the minimization problem \[ \min\left\{\int_{B_1}|Du|^2:\ u\in W^{1,2}(B_1;\mathbb R^n),\quad u=x\ \text{on }\partial B_1,\quad |u|\ge a\right\}, \quad 0<a<1. \] Figalli, Guerra, Kim, and Shahgholian proved that the canonical radial vortex is the unique global minimizer for $n\ge7$, and asked whether the same holds in dimensions \(3\le n \le6\). We answer this question affirmatively, thereby completing the global minimality and rigidity of the constraint map vortex in every dimension \(n\ge3\).

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Bin Deng, Jiahuan Li, Yilu Liu, Xi-Nan Ma. 2026-08-25. Global Minimality and Rigidity of the Constraint Map Vortex. https://arxiv.org/abs/2608.24805

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