The one-sided isometric extension problem

DOI10.1007/s00025-016-0593-0zbMath1380.53065arXiv1410.0232OpenAlexW1949781233MaRDI QIDQ2410819

Micha Wasem, Norbert Hungerbühler

Publication date: 19 October 2017

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.0232

zbMATH Keywords

isometric extension\(h\)-principleconvex integration

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Embeddings in differential topology (57R40) Local Riemannian geometry (53B20) Boundary value problems for systems of nonlinear first-order PDEs (35F60)

Related Items (8)

Very weak solutions to the two-dimensional Monge-Ampére equation ⋮ Rigidity and flexibility of isometric extensions ⋮ Geometric, algebraic, and analytic descendants of Nash isometric embedding theorems ⋮ C^1,α isometric extensions ⋮ An explicit isometric reduction of the unit sphere into an arbitrarily small ball ⋮ Equidimensional isometric extensions ⋮ \(C^{1, \alpha }\) isometric embeddings of polar caps ⋮ Global Nash-Kuiper theorem for compact manifolds

Cites Work

• The Taylor expansion of the exponential map and geometric applications
• The imbedding problem for Riemannian manifolds
• Equidimensional isometric maps
• Darboux equations and isometric embedding of Riemannian manifolds with nonnegative curvature in \(\mathbb{R}^3\)
• Extending isometric embeddings
• Radial part of Brownian motion on a Riemannian manifold
• \(C^1\) isometric imbeddings
• h-Principle and Rigidity for C 1,α Isometric Embeddings
• Partial Differential Relations
• The ℎ-principle and the equations of fluid dynamics
• Flat tori in three-dimensional space and convex integration
• Isometric embeddings
• Embeddings and immersions in Riemannian geometry
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