\(H\)-bubbles with prescribed large mean curvature (Q1424387)

For a smooth real-valued function \(H\) on \(\mathbb{R}^3\) an \(H\)-bubble is a conformally immersed 2-sphere with mean curvature \(H\) at every point. It is shown that for any nondegenerate stationary point \(p\) of \(H\) with \(H(p)\neq 0\) there exists a family of embedded \(tH\)-bubbles for large \(t\), which become round and concentrate at \(p\) for \(t\to\infty\). The nondegeneracy can be replaced by some kind of topological stability in case of extremal points. The proofs use a perturbation method.