Abstract
This paper is devoted to the study of a quantitative Weinstock inequality in higher dimension for the first non trivial Steklov eigenvalue of the Laplace operator for convex sets. The key role is played by a quantitative isoperimetric inequality which involves the boundary momentum, the volume and the perimeter of a convex open set of $${\mathbb {R}}^n$$, $$n \ge 2$$.
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