Weighted quantitative isoperimetric inequalities in the Grushin space {R}^{h+1} with density |x|^{p}

Abstract

In this paper, we prove weighted quantitative isoperimetric inequalities for the set E_{alpha}= {(x,y)in {R}^{h+1}: vert y vert <int_{arcsin vert x vert }^{frac{pi}{2}}sin^{alpha +1}(t),dt, vert x vert <1 } in half-cylinders in the Grushin space {R}^{h+1} with density vert x vert ^{p}, pgeq0.