On the stability of the annulus for the torsion of multiply connected domains

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2026年6月10日

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Vincenzo Amato,
Luca Barbato

摘要

We establish a quantitative version of the isoperimetric inequality for the torsional rigidity of multiply connected domains, among sets with given area and with given joint area of the holes. Since the optimal shape is the annulus, we study how a domain approaches an annular configuration when its torsional rigidity is close to optimal. Our result shows that when the torsional rigidity is nearly optimal, the domain $\Omega $ $Ω$ must be close to an annulus.