Regular homotopy and total curvature. I: Circle immersions into surfaces

DOI10.2140/agt.2006.6.459zbMath1113.53041arXivmath/0310266OpenAlexW96004544MaRDI QIDQ2492037

Tobias Ekholm

Publication date: 1 June 2006

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310266

zbMATH Keywords

total geodesic curvaturesphere eversiontotal Gauss curvaturecircle immersionsPGC curverelatively isotopy tight immersionsphere immersion

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Curves in Euclidean and related spaces (53A04) Immersions in differential topology (57R42)

Related Items (3)

Willmore minmax surfaces and the cost of the sphere eversion ⋮ Regular homotopy and total curvature. I: Circle immersions into surfaces ⋮ On the total absolute curvature of an immersed sphere

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The classification of immersions of spheres in Euclidean spaces
• Total curvature for knotted surfaces
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Riemannian geometry and geometric analysis.
• Invariants of types \(j^+,j^-\), and st for smooth curves on two-dimensional manifolds
• Regular homotopy and total curvature. I: Circle immersions into surfaces
• Convex immersions of closed surfaces in \(E^3\). Non-orientable closed surfaces in \(E^3\) with minimal total absolute Gauss-curvature
• A Classification of Immersions of the Two-Sphere
• Partial Differential Relations
• Immersions of Manifolds
• Arnold-type invariants of wave fronts on surfaces

This page was built for publication: Regular homotopy and total curvature. I: Circle immersions into surfaces