EXISTENCE OF MINIMAL H-BUBBLES

DOI10.1142/S021919970200066XzbMath1009.53008arXivmath/0006157MaRDI QIDQ4546067

Roberta Musina, Paolo Caldiroli

Publication date: 18 August 2002

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0006157

zbMATH Keywords

variational functionalprescribed mean curvatureclosed soap-bubble like surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Existence theories for free problems in two or more independent variables (49J10)

Related Items (14)

Existence of \(H\)-bubbles in a perturbative setting ⋮ Weak limit and blowup of approximate solutions to \(H\)-systems ⋮ Existence and multiplicity results for a weighted \(p\)-Laplace equation involving Hardy potentials and critical nonlinearities ⋮ Isovolumetric and isoperimetric problems for a class of capillarity functionals ⋮ Existence of isovolumetric \(\mathbb S^2\)-type stationary surfaces for capillarity functionals ⋮ On the regularity of weak solutions to \(H\)-system ⋮ Bubbles with prescribed mean curvature: the variational approach ⋮ \(H\)-bubbles in a perturbative setting: the finite-dimensional reduction method ⋮ The Dirichlet problem for \(H\)-systems with small boundary data: blowup phenomena and nonexistence results ⋮ Blow-up analysis for the prescribed mean curvature equation on \(\mathbb R^2\) ⋮ Planar loops with prescribed curvature: Existence, multiplicity and uniqueness results ⋮ The role of the spectrum of the Laplace operator on \(\mathbb S^2\) in the \(\mathcal H\) bubble problem ⋮ A note on the existence of \(H\)-bubbles via perturbation methods ⋮ On the non-existence of compact surfaces of genus one with prescribed, almost constant mean curvature, close to the singular limit

Cites Work

• Convergence of solutions of H-systems or how to blow bubbles
• The existence of minimal immersions of 2-spheres
• On the existence of surfaces with prescribed mean curvature and boundary
• Isoperimetric inequalities and the problem of Plateau
• Multiple solutions to the Plateau problem for nonconstant mean curvature
• Multiple surfaces of non-constant mean curvature
• Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. I: Fest vorgegebener Rand
• Multiple solutions ofH-systems and Rellich's conjecture
• Two‐dimensional variational problems with obstructions, and Plateau's problem for h‐surfaces in a riemannian manifold

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