# Questions tagged [implicit-function-theorem]

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### Implicit function theorem with continuous dependence on parameter

Let $X,Y$ be Hilbert spaces and $P$ a topological space$^1$ and $p_0\in P$. Let $f:X\times P\to Y$ be a continuous map such that for any parameter $p\in P$, $f_p:= f|_{X\times \{p\}}:X\to Y$ is ...
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### Is there a version of Hamilton's infinite dimensional family of implicit function theorems which gives us a submersion map?

Hamilton, in his notes on "Inverse Function Theorem of Nash and Moser" states a theorem(1.1.3 on Page 172), where a given nonlinear map between tame Frechet spaces is locally surjective, if ...
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### Question about the implicit function theorem. an example of a homogeneous form for which its implicit function satisfies certain conditions

Let $F$ be a homogeneous form with coefficients in $\mathbb{R}$. Suppose it defines a smooth projective variety, in other words at every point other than the origin at least one of the first partial ...
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### Tangent space of smooth Hilbert submanifolds

Let $X, Y$ be Hilbert spaces and $F:X \rightarrow Y$ smooth. Assume that $M := F^{-1}(0) \subset X$ is a smooth submanifold. Is it true that for any $x\in M$, the tangent space $T_xM$ is a Hilbert ...
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### Implicit function theorem for subdifferentiable convex functions

I am trying to find a method to apply the implicit function theorem for subdifferential convex functions. The original theorem provides an equation for the partial derivative of the implicit function ...