Question

Is monotonicity a necessary condition for the inverse function theorem?

score 1k · Answer 1 · 2026-03-26 01:01:49

1k

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Is monotonicity a necessary condition for the inverse function theorem?

Published on 26 Mar 2026 - 1:01

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 368 · Answer 4 · 2026-03-26 01:04:48

368

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 26 Mar 2026 - 1:04

score 840 · Answer 5 · 2026-03-26 01:03:01

840

Views

Assumptions of the inverse mapping theorem

Published on 26 Mar 2026 - 1:03

score 171 · Answer 6 · 2026-03-26 01:00:20

171

Views

Find affine function to approximate local inverse

Published on 26 Mar 2026 - 1:00

score 55 · Answer 7 · 2026-03-26 01:06:14

55

Views

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

Published on 26 Mar 2026 - 1:06

score 356 · Answer 8 · 2026-03-26 01:04:48

356

Views

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

Published on 26 Mar 2026 - 1:04

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 38 · Answer 10 · 2026-03-26 01:03:28

38

Views

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

Published on 26 Mar 2026 - 1:03

score 1k · Answer 11 · 2026-03-26 01:06:38

1k

Views

inverse function theorem and matrix square root

Published on 26 Mar 2026 - 1:06

score 116 · Answer 12 · 2026-03-26 01:04:49

116

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 26 Mar 2026 - 1:04

score 1.2k · Answer 13 · 2026-03-26 01:07:55

1.2k

Views

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

Published on 26 Mar 2026 - 1:07

score 38 · Answer 14 · 2026-05-04 02:52:43

38

Views

Implicit function for quadrants of real Banach space

Published on 04 May 2026 - 2:52

score 353 · Answer 15 · 2026-03-26 01:00:03

353

Views

Example appliction of Nash-Moser inverse function theorem

Published on 26 Mar 2026 - 1:00

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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