The imbedding problem for Riemannian manifolds

By J. Nash. 1956

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Citations in the corpus

On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds (2007, methodology): “To this aim we remark that by Nash embedding theorem [14], without loss of generality, we may assume that M is embedded in a Euclidean space R .”
Editors' Note on Packing Lines, Planes, etc.: Packings in Grassmannian Spaces (2002, unknown): “(Nor does the Nash embedding theorem [34].”
Ricci flow coupled with harmonic map flow (2009, methodology): “According to Nash’s embedding theorem [30] we can assume that N is isometrically embedded into Euclidean space (N, γ) →֒ R for a sufficiently large d.”
Differential Geometry of Special Mappings (2019, background): “An immersion V2 in Euclidean space is studied in detail, for example, in [146, 718].”
Well-posedness of the Prandtl equation in Sobolev spaces (2012, unknown): “[1, 10, 13, 16, 17]) to study the nonlinear problem (1.”
Smoothness Analysis of Subdivision Schemes by Proximity (2006, methodology): “These results can be extended to abstract Riemannian manifolds and to a certain class of abstract Lie groups by using Nash’s embedding theorem for Riemannian manifolds [15] and by considering Lie groups which are locally isomorphic to matrix Lie groups of constant velocity.”
Rough solutions for the wave maps equation (2005, background): “If M is compact then such an embedding always exists by Nash’s theorem [15] (see also Gromov [5] and Günther [6]).”
Landau Damping: Paraproducts and Gevrey Regularity (2013, background): “Nash’s isometric embedding theorem [68] by Günther [34–36]), with maybe the only exception being KAM theory.”
Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions (2009, background): “Such an embedding always exists by Nash’s theorem [18] (see also Gromov [3] and Günther [4]).”