Existence of H-bubbles in a perturbative setting

Caldiroli, Paolo; Musina, Roberta

Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, p. 611-626 / Harvested from Project Euclid

Résumé

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.

Publié le : 2004-06-14
Classification: parametric surfaces, prescribed mean curvature, 53A10, 49J10

@article{1087482028,
     author = {Caldiroli, Paolo and Musina, Roberta},
     title = {Existence of H-bubbles in a perturbative setting},
     journal = {Rev. Mat. Iberoamericana},
     volume = {20},
     number = {1},
     year = {2004},
     pages = { 611-626},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087482028}
}

Caldiroli, Paolo; Musina, Roberta. Existence of H-bubbles in a perturbative setting. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp.  611-626. http://gdmltest.u-ga.fr/item/1087482028/