Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded...

applications in various sciences. In the 1950s, Nash discovered and proved the Nash embedding theorems by solving a system of nonlinear partial differential...

mathematics, Nash's theorem may refer to one of the following: the Nash embedding theorems in differential geometry Nash's theorem on the existence of Nash equilibria...

topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real m-dimensional...

geometry, an isometric embedding (immersion) is a smooth embedding (immersion) that preserves length of curves (cf. Nash embedding theorem). In general, for...

plane cannot be isometrically embedded into Euclidean 3-space by Hilbert's theorem. On the other hand the Nash embedding theorem implies that hyperbolic n-space...

ISSN 0002-5240. S2CID 253600065. Freyd–Mitchell embedding theorem at the nLab "Notes on the Nash embedding theorem". What's new. 2016-05-11. Retrieved 2019-12-08...

This theorem has a generalization to any compact even-dimensional Riemannian manifold, see generalized Gauss-Bonnet theorem. Nash embedding theorems. They...

This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures...

function theorem cannot be used. The Nash–Moser theorem traces back to Nash (1956), who proved the theorem in the special case of the isometric embedding problem...

Günther, Matthias (1989). "Zum Einbettungssatz von J. Nash" [On the embedding theorem of J. Nash]. Mathematische Nachrichten (in German). 144: 165–187...

integral theorem Computational geometry Fundamental theorem of algebra Lambda calculus Invariance of domain Minkowski inequality Nash embedding theorem Open...

revolutionary work of John Nash in differential geometry and partial differential equations, such as the Nash embedding theorem or his proof of Hilbert's...

used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly...

tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. A finitary...

if the Nash embedding theorem can be assumed. However, this theorem was not available then, as John Nash published his famous embedding theorem for Riemannian...

notions of isometric embeddings, isometric immersions, and Riemannian submersions; a basic result is the Nash embedding theorem. A basic example of maps...

under which it is developable, which can be embedded into three-dimensional space by the Nash embedding theorem and has a simple representation in four dimensions...

Whitney–Graustein theorem. This was followed by the Nash–Kuiper isometric C1 embedding theorem and the Smale–Hirsch immersion theorem. Assume we want to...

Embedding Whitney embedding theorem Critical value Sard's theorem Saddle point Morse theory Lie derivative Hairy ball theorem Poincaré–Hopf theorem Stokes'...

Moore's law Computing Gordon Moore Nash embedding theorem Nash equilibrium Topology Game Theory John Forbes Nash Nernst equation Electrochemistry Walther...

embedding of a torus in three-dimensional Euclidean space, the square torus can also be embedded into three-dimensional space, by the Nash embedding theorem;...

Nash–Moser theorems. In 1982, Hamilton published his formulation of Nash's reasoning, casting the theorem into the setting of tame Fréchet spaces; Nash's fundamental...

and immersions include: Whitney embedding theorem Whitney immersion theorem Nash embedding theorem Smale-Hirsch theorem Key tools in studying these maps...

notions of isometric embeddings, isometric immersions, and Riemannian submersions; a basic result is the Nash embedding theorem. A basic example of maps...

hand, the Nash embedding theorem states that, given any smooth Riemannian manifold ( M , g ) , {\displaystyle (M,g),} there is an embedding F : M → R...

known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem. Kuiper studied at University of Leiden in 1937-41...

Forbes Nash Jr. (1928–2015) United States Princeton University (PhD, mathematics) Princeton University Nash equilibrium, Nash embedding theorem, Nash functions...

an isometric embedding into R n {\displaystyle \mathbb {R} ^{n}} according to the Nash embedding theorem (Nash (1956)), but the embedding dimension is...

considered as a structure additional to the intrinsic one. (See the Nash embedding theorem.) In the formalism of geometric calculus both extrinsic and intrinsic...