2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78249Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensions using hyperbolic symmetry and conformal geometry.11 pages, AMSTeXAnalysis of PDEs58G30, 46E35text