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searching for Implicit function theorem 13 found (84 total)

alternate case: implicit function theorem

Nash functions (714 words) [view diff] exact match in snippet view article find links to article

Nash functions are those functions needed in order to have an implicit function theorem in real algebraic geometry. Along with Nash functions one defines

Nash–Moser theorem (3,545 words) [view diff] exact match in snippet view article find links to article

derivative "loses" derivatives, and therefore the Banach space implicit function theorem cannot be used. The Nash–Moser theorem traces back to Nash (1956)

Steven G. Krantz (1,943 words) [view diff] exact match in snippet view article find links to article

oscillation, geometric measure theory, sets of positive reach, the implicit function theorem, approximation theory, real analytic functions, analysis on the

Diffeomorphism (4,165 words) [view diff] exact match in snippet view article find links to article

Superdiffeomorphism Steven G. Krantz; Harold R. Parks (2013). The implicit function theorem: history, theory, and applications. Springer. p. Theorem 6.2.4

Algebraic space (1,588 words) [view diff] exact match in snippet view article find links to article

quotient stack). Artin 1969; Artin 1971. Artin, Michael (1969), "The implicit function theorem in algebraic geometry", in Abhyankar, Shreeram Shankar (ed.),

Gauss's lemma (Riemannian geometry) (2,176 words) [view diff] exact match in snippet view article

differential of exp p {\displaystyle \exp _{p}} is the identity. By the implicit function theorem, exp p {\displaystyle \exp _{p}} is a diffeomorphism on a neighborhood

Ricci flow (7,777 words) [view diff] exact match in snippet view article find links to article

metric on M {\displaystyle M} . Making use of the Nash–Moser implicit function theorem, Hamilton (1982) showed the following existence theorem: There

Zlil Sela (1,850 words) [view diff] exact match in snippet view article find links to article

vol. 4 (1998), pp. 101–108 O. Kharlampovich, and A. Myasnikov. Implicit function theorem over free groups. Journal of Algebra, vol. 290 (2005), no. 1,

Convenient vector space (4,008 words) [view diff] exact match in snippet view article find links to article

{\displaystyle f(t,f(t,\quad )^{-1}(x))=x} , so by the finite dimensional implicit function theorem, ( t , x ) ↦ f ( t , ) − 1 ( x ) {\displaystyle (t,x)\mapsto

Mikhael Gromov (mathematician) (3,749 words) [view diff] exact match in snippet view article

work building upon Nash and Kuiper's theorem and the Nash–Moser implicit function theorem. There are many applications of his results, including topological

Automatic differentiation (6,047 words) [view diff] case mismatch in snippet view article find links to article

differentiation). Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem C++ Template-based automatic differentiation article and implementation

Differentiable manifold (9,509 words) [view diff] exact match in snippet view article find links to article

has rank n at p ∈ M, then f is called a submersion at p. The implicit function theorem states that if f is a submersion at p, then M is locally a product

Function of several complex variables (17,591 words) [view diff] exact match in snippet view article find links to article

function theorems also hold. For a generalized version of the implicit function theorem to complex variables, see the Weierstrass preparation theorem