Closed curves in \((\mathbb R^3)\) with prescribed curvature and torsion in perturbative cases. I: Necessary condition and study of the unperturbed problem

DOI10.4171/RLM/466zbMath1229.53004MaRDI QIDQ997575

Paolo Caldiroli, Michela Guida

Publication date: 7 August 2007

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

zbMATH Keywords

Fredholm operatorsperturbative methodsprescribed curvature and torsion

Mathematics Subject Classification ID

(Semi-) Fredholm operators; index theories (47A53) Curves in Euclidean and related spaces (53A04)

Related Items (2)

Closed curves in \((\mathbb{R}^{3})\) with prescribed curvature and torsion in perturbative cases. Part 2: Sufficient conditions ⋮ Planar loops with prescribed curvature: Existence, multiplicity and uniqueness results

Cites Work

• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
• A multiplicity result for the Yamabe problem on \(S^n\)

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