Planar loops with prescribed curvature: Existence, multiplicity and uniqueness results

DOI10.1090/S0002-9939-2011-10915-8zbMath1242.53004MaRDI QIDQ3104465

Roberta Musina

Publication date: 13 December 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

loopminimal energyprescribed curvaturespace of periodic functions

Mathematics Subject Classification ID

Existence theories for free problems in two or more independent variables (49J10) Curves in Euclidean and related spaces (53A04)

Related Items (4)

An inverse approach to hyperspheres of prescribed mean curvature in Euclidean space ⋮ The normal derivative lemma and surrounding issues ⋮ On the dynamics of a charged particle in magnetic fields with cylindrical symmetry ⋮ Embedded loops in the hyperbolic plane with prescribed, almost constant curvature

Cites Work

• Bubbles with prescribed mean curvature: the variational approach
• Symmetric \(\kappa \)-loops.
• Embedded hyperspheres with prescribed mean curvature
• Helicoidal trajectories of a charge in a nonconstant magnetic field
• Closed curves in \((\mathbb R^3)\) with prescribed curvature and torsion in perturbative cases. I: Necessary condition and study of the unperturbed problem
• Convergence of solutions of H-systems or how to blow bubbles
• The strong maximum principle revisited.
• The Four-or-More Vertex Theorem
• EXISTENCE OF MINIMAL H-BUBBLES
• On the Uniqueness of Compact Solutions for Certain Elliptic Differential Equations
• Uniqueness theorems for surfaces in the large. I, II, III, IV, V

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