H-bubbles with prescribed large mean curvature

Given a smooth function $H\colon\mathbb{R}^{3}\to\mathbb{R}$, we call $H$-bubble a conformally immersed surface in $\mathbb{R}^{3}$ parametrized on the sphere $\mathbb{S}^{2}$ with mean curvature $H$ at every point. We prove that if $\bar p\in\mathbb{R}^{3}$ is a nondegenerate stationary point for $H$ with $H(\bar p)\ne 0$, then there exists a curve $\theta\mapsto u^{\theta}$ of embedded $\theta H$-bubbles, defined for $\theta$ large, which become round and concentrate at $\bar{p}$ as $\theta\to+\infty$. Also the case of topologically stable extremal points for $H$ is considered.