JournalsrmiVol. 20, No. 2pp. 611–626

Existence of H-bubbles in a perturbative setting

  • Paolo Caldiroli

    Università degli Studi di Torino, Italy
  • Roberta Musina

    Università di Udine, Italy
Existence of H-bubbles in a perturbative setting cover
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Abstract

Given a C1C^{1} function H:R3RH: \mathbb{R}^3 \to \mathbb{R}, we look for HH-bubbles, i.e., surfaces in R3\mathbb{R}^3 parametrized by the sphere S2\mathbb{S}^2 with mean curvature HH at every regular point. Here we study the case H(u)=H0(u)+ϵH1(u)H(u)=H_{0}(u)+\epsilon H_{1}(u) where H0H_{0} is some "good" curvature (for which there exist H0H_{0}-bubbles with minimal energy, uniformly bounded in LL^{\infty}), ϵ\epsilon is the smallness parameter, and H1H_{1} is {\em any} C1C^{1} function.

Cite this article

Paolo Caldiroli, Roberta Musina, Existence of H-bubbles in a perturbative setting. Rev. Mat. Iberoam. 20 (2004), no. 2, pp. 611–626

DOI 10.4171/RMI/402