Sobolev spaces of isometric immersions of arbitrary dimension and co-dimension

DOI10.1007/s10231-016-0591-6zbMath1375.35235arXiv1405.4765OpenAlexW1744831645MaRDI QIDQ522161

Mohammad Reza Pakzad, Robert Leon Jerrard

Publication date: 13 April 2017

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.4765

zbMATH Keywords

Monge-Ampère equationsrigidity of isometric immersionsSobolev spaces of mappings

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Spaces of embeddings and immersions (58D10) Rigidity results (53C24) Monge-Ampère equations (35J96) Geometric embeddings of metric spaces (30L05)

Related Items (6)

A strictly convex Sobolev function with null Hessian minors ⋮ Uniqueness of the critical point for solutions of some \(p\)-Laplace equations in the plane ⋮ Stability of isometric immersions of hypersurfaces ⋮ Convex integration for the Monge-Ampère equation in two dimensions ⋮ Approximation by mappings with singular Hessian minors ⋮ Visualization of the convex integration solutions to the Monge-Ampère equation

Cites Work

• Convex integration for the Monge-Ampère equation in two dimensions
• Approximation of flat \(W ^{2,2}\) isometric immersions by smooth ones
• Fine level set structure of flat isometric immersions
• On the Sobolev space of isometric immersions
• Approximating \(W^{2,2}\) isometric immersions
• Continuity of Bessel potentials
• Regularity properties of isometric immersions
• A strictly convex Sobolev function with null Hessian minors
• \(C^1\) isometric imbeddings
• Limitations on the smooth confinement of an unstretchable manifold
• h-Principle and Rigidity for C 1,α Isometric Embeddings
• Scaling laws for non-Euclidean plates and theW^2,2isometric immersions of Riemannian metrics
• On the Total Curvature of Immersed Manifolds
• On Spherical Image Maps Whose Jacobians Do Not Change Sign
• Rigidity and regularity of co-dimension one Sobolev isometric immersions
• Some Rigidity Results Related to Monge–Ampèere Functions
• Weakly Differentiable Functions
• Lusin's condition (N) and mappings of the class W1, n.
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
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