A note on the existence of H-bubbles via perturbation methods

2003/01/23 by Veronica Felli, Felli, Veronica
Mathematics · #35B20 #35J50 #53A10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35B20 #msc:35J50 #msc:53A10

paper · pdf · doi:10.48550/arxiv.math/0301265

14 pages

openalex publication_date 2003/01/23 · arxiv created 2003/01/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of existence of surfaces in \bf R³ parametrized on the sphere \mathbb S² with prescribed mean curvature H in the perturbative case, i.e. for H=H₀+εH₁, where H₀ is a nonzero constant, H₁ is a C² function and ε is a small perturbation parameter.

Related

• Existence of minimal H-bubbles
• Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space
• Compact surfaces with boundary with prescribed mean curvature depending on the Gauss map
• Existence of free boundary disks with constant mean curvature in ℝ³
• The harmonic mean curvature flow of nonconvex surfaces in ℝ³