\(C^{1,1-\varepsilon}\) isometric embeddings
type: Item
instance of: scholarly article
title: \(C^{1,1-\varepsilon}\) isometric embeddings
zbMATH Open document ID: 1546.5306
author: Ángel D. Martínez
published in: Transactions of the American Mathematical Society
publication date: 2024-07-12T00:00:00Z
review text: This paper is devoted to the construction of isometric emebeddings of \(n\)-dimensional manifolds in codimension \(1+n(n+1)/2\). The techniques of convex integration as well as ideas of \textit{A. Källen} [Ark. Mat. 16, 29--50 (1978; Zbl 0381.35014)] and \textit{H. Kröner} [``Irregular Isometric Embeddings of Compact Manifolds'', Master Thesis Mathematics, Institute for Applied Mathematics (2012)] are used to improve results on the regularity of these isometric embeddings.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58A20
zbMATH DE Number: 7880403
zbMATH Keywords: isometric embeddings
zbMATH Keywords: local \(h\)-principle
zbMATH Keywords: Nash-Kuiper theorem
zbMATH Keywords: convex integration
MaRDI profile type: Publication
cites work: Q4811812
cites work: Anomalous dissipation for \(1/5\)-Hölder Euler flows
cites work: Onsager's Conjecture for Admissible Weak Solutions
cites work: C1,α isometric extensions
cites work: Very weak solutions to the two-dimensional Monge-Ampére equation
cites work: The immersion conjecture for differentiable manifolds
cites work: h-Principle and Rigidity for C 1,α Isometric Embeddings
cites work: A Nash-Kuiper theorem for \(C^{1,\frac{1}{5}-\delta}\) immersions of surfaces in 3 dimensions
cites work: \(C^{1, \alpha }\) isometric embeddings of polar caps
cites work: The ℎ-principle and the equations of fluid dynamics
cites work: Dissipative continuous Euler flows
cites work: High dimensionality and h-principle in PDE
cites work: On turbulence and geometry: from Nash to Onsager
cites work: Geometric, algebraic, and analytic descendants of Nash isometric embedding theorems
cites work: Q5599507
cites work: On the perturbation problem associated to isometric embeddings of Riemannian manifolds
cites work: Q4011217
cites work: A proof of Onsager's conjecture
cites work: Isometric embedding of a smooth compact manifold with a metric of low regularity
cites work: On Nash’s unique contribution to analysis in just three of his papers
cites work: Q3229047
cites work: \(C^1\) isometric imbeddings
cites work: The imbedding problem for Riemannian manifolds
cites work: Q4069454
cites work: Isometric embedding of flat manifolds in Euclidean space
cites work: Differentiable manifolds.
DOI: 10.1090/TRAN/9086
description: scientific article; zbMATH DE number 7880403