Open Access
June, 2004 Existence of H-bubbles in a perturbative setting
Paolo Caldiroli, Roberta Musina
Rev. Mat. Iberoamericana 20(2): 611-626 (June, 2004).


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.


Download Citation

Paolo Caldiroli. Roberta Musina. "Existence of H-bubbles in a perturbative setting." Rev. Mat. Iberoamericana 20 (2) 611 - 626, June, 2004.


Published: June, 2004
First available in Project Euclid: 17 June 2004

zbMATH: 1066.53018
MathSciNet: MR2073133

Primary: 49J10 , 53A10

Keywords: parametric surfaces , prescribed mean curvature

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.20 • No. 2 • June, 2004
Back to Top