Revista Matemática Iberoamericana

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Volume 20, Issue 2, 2004, pp. 611–626
DOI: 10.4171/RMI/402

Published online: 2004-08-31

Existence of H-bubbles in a perturbative setting

Paolo Caldiroli[1] and Roberta Musina[2]

(1) Università degli Studi di Torino, Italy
(2) Università di Udine, Italy

Given a $C^{1}$ function $H: \mathbb{R}^3 \to \mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\mathbb{R}^3$ parametrized by the sphere $\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\epsilon H_{1}(u)$ where $H_{0}$ is some "good" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\infty}$), $\epsilon$ is the smallness parameter, and $H_{1}$ is {\em any} $C^{1}$ function.

Keywords: Parametric surfaces, prescribed mean curvature

Caldiroli Paolo, Musina Roberta: Existence of H-bubbles in a perturbative setting. Rev. Mat. Iberoamericana 20 (2004), 611-626. doi: 10.4171/RMI/402