2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66334We study the problem of existence of surfaces in ${\bf R}^3$ parametrized on the sphere ${\mathbb S}^2$ with prescribed mean curvature $H$ in the perturbative case, i.e. for $H=H_0+εH_1$, where $H_0$ is a nonzero constant, $H_1$ is a $C^2$ function and $ε$ is a small perturbation parameter.14 pagesAnalysis of PDEsDifferential Geometry53A10, 35J50, 35B20text