Question

Is monotonicity a necessary condition for the inverse function theorem?

score 1k · Answer 1 · 2020-06-02 04:02:37

1k

Views

Is monotonicity a necessary condition for the inverse function theorem?

Published on 02 Jun 2020 - 4:02

score 634 · Answer 2 · 2026-03-25 18:53:41

634

Views

Is the parameterization of a regular surface a local diffeomorphism?

Published on 25 Mar 2026 - 18:53

score 239 · Answer 3 · 2026-03-25 17:17:26

239

Views

is a diffeomorphism regular?

Published on 25 Mar 2026 - 17:17

score 367 · Answer 4 · 2020-06-15 15:45:25

367

Views

If $f:U\to\mathbb{R}^N$ is a $C^k$-submersion, $g:f(U)\to \mathbb{R}^M$ and $g\circ f :U\to\mathbb{R}^M$ is $C^k$ then $g$ is $C^k$

Published on 15 Jun 2020 - 15:45

score 839 · Answer 5 · 2020-06-26 06:44:00

839

Views

Assumptions of the inverse mapping theorem

Published on 26 Jun 2020 - 6:44

score 170 · Answer 6 · 2020-06-30 01:15:44

170

Views

Find affine function to approximate local inverse

Published on 30 Jun 2020 - 1:15

score 54 · Answer 7 · 2020-07-03 05:37:58

54

Views

Inverse function of $f(x)=e^x+x-1$.

Published on 03 Jul 2020 - 5:37

score 355 · Answer 8 · 2020-07-16 22:14:51

355

Views

Show that there exists a neighborhood $U$ of $(0,1)$ such that the restriction $g:U \rightarrow g[U]$ is invertible

Published on 16 Jul 2020 - 22:14

score 115 · Answer 9 · 2026-03-25 19:07:14

115

Views

If $T_t$ is a diffeomorphism and $t\mapsto T_t(x)$ is differentiable, can we find a map $v$ with $v(t,T_t(x))=\frac{\partial T}{\partial t}(t,x)$?

Published on 25 Mar 2026 - 19:07

score 37 · Answer 10 · 2020-07-31 01:51:15

37

Views

How do I show If $f(B_r)$ is in a rectangle with side $Mr$ and $ \epsilon r$.

Published on 31 Jul 2020 - 1:51

score 1k · Answer 11 · 2026-03-22 14:16:12

1k

Views

inverse function theorem and matrix square root

Published on 22 Mar 2026 - 14:16

score 115 · Answer 12 · 2026-03-20 22:47:52

115

Views

Find conditions on $x$ and $y$ which guarantee that one can locally solve the following for $u(x, y)$ and $v(x, y)$

Published on 20 Mar 2026 - 22:47

score 1.2k · Answer 13 · 2026-03-22 12:14:57

1.2k

Views

Jacobian determinant of a function $f$ if it has a differentiable inverse.

Published on 22 Mar 2026 - 12:14

score 32 · Answer 14 · 2026-03-21 18:36:04

32

Views

Implicit function for quadrants of real Banach space

Published on 21 Mar 2026 - 18:36

score 352 · Answer 15 · 2026-03-22 09:42:18

352

Views

Example appliction of Nash-Moser inverse function theorem

Published on 22 Mar 2026 - 9:42

List Question

Is monotonicity a necessary condition for the inverse function theorem?

Is the parameterization of a regular surface a local diffeomorphism?

is a diffeomorphism regular?

If $f:U\to\mathbb{R}^N$ is a $C^k$-submersion, $g:f(U)\to \mathbb{R}^M$ and $g\circ f :U\to\mathbb{R}^M$ is $C^k$ then $g$ is $C^k$

Assumptions of the inverse mapping theorem

Find affine function to approximate local inverse

Inverse function of $f(x)=e^x+x-1$.

Show that there exists a neighborhood $U$ of $(0,1)$ such that the restriction $g:U \rightarrow g[U]$ is invertible

If $T_t$ is a diffeomorphism and $t\mapsto T_t(x)$ is differentiable, can we find a map $v$ with $v(t,T_t(x))=\frac{\partial T}{\partial t}(t,x)$?

How do I show If $f(B_r)$ is in a rectangle with side $Mr$ and $ \epsilon r$.

inverse function theorem and matrix square root

Find conditions on $x$ and $y$ which guarantee that one can locally solve the following for $u(x, y)$ and $v(x, y)$

Jacobian determinant of a function $f$ if it has a differentiable inverse.

Implicit function for quadrants of real Banach space

Example appliction of Nash-Moser inverse function theorem

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