The role of the spectrum of the Laplace operator on \(\mathbb S^2\) in the \(\mathcal H\) bubble problem

DOI10.1007/BF02789050zbMath1129.58300MaRDI QIDQ2565885

Roberta Musina

Publication date: 28 September 2005

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for second-order elliptic equations (35J20) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (9)

Radial graphs over domains of \(\mathbb S^n\) with prescribed mean curvature ⋮ 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 ⋮ Embedded loops in the hyperbolic plane with prescribed, almost constant curvature ⋮ Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space ⋮ EMBEDDED DISC-TYPE SURFACES WITH LARGE CONSTANT MEAN CURVATURE AND FREE BOUNDARIES ⋮ Bubbles with prescribed mean curvature: the variational approach ⋮ \(H\)-bubbles in a perturbative setting: the finite-dimensional reduction method

Cites Work

• Unnamed Item
• Unnamed Item
• \(H\)-bubbles in a perturbative setting: the finite-dimensional reduction method
• Convergence of solutions of H-systems or how to blow bubbles
• Isoperimetric inequalities and the problem of Plateau
• \(H\)-bubbles with prescribed large mean curvature
• Existence of \(H\)-bubbles in a perturbative setting
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• A note on the existence of \(H\)-bubbles via perturbation methods
• Asymptotic Morse theory for the equation \(\Delta v- 2v_x\wedge v_y\)
• Multiple solutions ofH-systems and Rellich's conjecture
• Variational perturbative methods and bifurcation of bound states from the essential spectrum
• EXISTENCE OF MINIMAL H-BUBBLES
• On the asymptotic analysis of \(H\)-systems. I: Asymptotic behavior of large solutions.
• On the asymptotic analysis of \(H\)-systems. II: The construction of large solutions

This page was built for publication: The role of the spectrum of the Laplace operator on \(\mathbb S^2\) in the \(\mathcal H\) bubble problem