List questions from inverse-function-theorem

Published on 20 Mar 2026 - 0:35

65

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Function satisfying $(Df(x)h,h) \geq \alpha(h,h), \forall x,h \in \mathbb{R}^n$ has an inverse around every point?

Published on 23 Mar 2026 - 6:50

71

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Prove for all point $(x_0,y_0)\not =(0,0)$ the restriction of $f$ to neighborhood $(x_0,y_0)$ have inverse.

Published on 23 Mar 2026 - 6:46

65

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Question on the proof of the inverse function theorem

Published on 22 Mar 2026 - 22:40

314

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Find Jacobian and rank of differential. Inverse function theorem.

Published on 22 Mar 2026 - 18:43

784

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Is a continuously differentiable bi-Lipschitz map on $\mathbf R^d$ a $C^1$-diffeomorphism?

Published on 22 Mar 2026 - 19:04

152

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Application of the Inverse function theorem for $f:M_n(\mathbb{R})\rightarrow M_n(\mathbb{R})$, $f(A)=A^2$.

Published on 22 Mar 2026 - 23:50

349

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Explanation of "without loss of generality" in an application of Inverse Function Theorem.

Published on 23 Mar 2026 - 5:39

26

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If $F(x+y,x/y)=0$ for $F$ smooth and $(x,y)$ in any open subset of $\mathbb{R}^2$, then $F=0$ on an open subset.

Published on 22 Mar 2026 - 14:18

183

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Laplacian of the inverse of a diffeomorphism

Published on 22 Mar 2026 - 20:26

124

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Should the points in the fiber lie in different connected component?

Published on 23 Mar 2026 - 0:38

150

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How do I set up Implicit Function Theorem to verify this function is a $C^{r}$ diffeomorphism?

Published on 25 Mar 2026 - 1:14

47

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Inverse Function Theorem Problem Feedback

Published on 21 Mar 2026 - 17:18

122

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Question about Spivaks Inverse function theorem proof

Published on 25 Mar 2026 - 4:35

116

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Is $f$ globally invertible on $R^2$?

Published on 25 Mar 2026 - 4:40

List Question

Inverse function theorem via degree theory

Function satisfying $(Df(x)h,h) \geq \alpha(h,h), \forall x,h \in \mathbb{R}^n$ has an inverse around every point?

Prove for all point $(x_0,y_0)\not =(0,0)$ the restriction of $f$ to neighborhood $(x_0,y_0)$ have inverse.

Question on the proof of the inverse function theorem

Find Jacobian and rank of differential. Inverse function theorem.

Is a continuously differentiable bi-Lipschitz map on $\mathbf R^d$ a $C^1$-diffeomorphism?

Application of the Inverse function theorem for $f:M_n(\mathbb{R})\rightarrow M_n(\mathbb{R})$, $f(A)=A^2$.

Explanation of "without loss of generality" in an application of Inverse Function Theorem.

If $F(x+y,x/y)=0$ for $F$ smooth and $(x,y)$ in any open subset of $\mathbb{R}^2$, then $F=0$ on an open subset.

Laplacian of the inverse of a diffeomorphism

Should the points in the fiber lie in different connected component?

How do I set up Implicit Function Theorem to verify this function is a $C^{r}$ diffeomorphism?

Inverse Function Theorem Problem Feedback

Question about Spivaks Inverse function theorem proof

Is $f$ globally invertible on $R^2$?

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