List questions from diffeomorphism

Published on 13 Apr 2026 - 18:14

1.9k

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Is every diffeomorphism an open map?

Published on 11 Apr 2026 - 14:42

205

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One line proof - the jacobian is sometimes $1$ or $-1$

Published on 15 Apr 2026 - 17:49

484

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Twice contracted Bianchi identity from diffeomorphism invariance

Published on 29 Apr 2026 - 12:51

202

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Persistence of elliptic / parabolic fixed points of maps and flows

Published on 29 Apr 2026 - 12:52

266

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Show $\mathbb{R}^n$ is not diffeomorphic to $\mathbb{R}^m$ for $m\neq n$

Published on 16 Apr 2026 - 11:27

48

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Need a counter example for tangent map preserving inner product, but F is not isometry

Published on 10 Apr 2026 - 2:37

154

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

Published on 29 Apr 2026 - 12:54

66

Views

In $\Bbb R^3$, If tangent map of F preserves inner product, then F is an isometry?

Published on 15 Apr 2026 - 12:16

149

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Structural stability in orientation preserving $[0,1]$ diffeomorphism

Published on 10 Apr 2026 - 5:46

1.5k

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$F$ is local diffeomorphism $\Leftrightarrow$ $F$ preserves or reverses orientation.

Published on 17 Apr 2026 - 12:21

366

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Proof that $\text{Diff}(M)$ is a topological group

Published on 14 Apr 2026 - 17:18

136

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Definition of hyperbolic set in dynamical systems

Published on 11 Apr 2026 - 0:57

74

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Level curve and PDE

Published on 16 Apr 2026 - 6:32

55

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How to show that $[c_i, d_i] \subset [a_i- \lambda, b_i + \lambda]$?

Published on 12 Apr 2026 - 1:36

List Question

Interpretation for diffeomorphism

Is every diffeomorphism an open map?

One line proof - the jacobian is sometimes $1$ or $-1$

Twice contracted Bianchi identity from diffeomorphism invariance

Persistence of elliptic / parabolic fixed points of maps and flows

Show $\mathbb{R}^n$ is not diffeomorphic to $\mathbb{R}^m$ for $m\neq n$

Need a counter example for tangent map preserving inner product, but F is not isometry

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

In $\Bbb R^3$, If tangent map of F preserves inner product, then F is an isometry?

Structural stability in orientation preserving $[0,1]$ diffeomorphism

$F$ is local diffeomorphism $\Leftrightarrow$ $F$ preserves or reverses orientation.

Proof that $\text{Diff}(M)$ is a topological group

Definition of hyperbolic set in dynamical systems

Level curve and PDE

How to show that $[c_i, d_i] \subset [a_i- \lambda, b_i + \lambda]$?

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