Question

A possible geometric inequality on Jacobian integrals of diffeomorphisms

score 23 · Answer 1 · 2017-08-01 22:12:32

23

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A possible geometric inequality on Jacobian integrals of diffeomorphisms

Published on 01 Aug 2017 - 22:12

score 753 · Answer 2 · 2017-08-02 00:24:53

753

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The canonical projection $\mathbb{S}^n\twoheadrightarrow\mathbb{R}P^n$ is a local diffeomorphism.

Published on 02 Aug 2017 - 0:24

score 50 · Answer 3 · 2017-08-08 09:53:44

50

Views

Can diffeomorphisms only be defined on real manifolds?

Published on 08 Aug 2017 - 9:53

score 1.1k · Answer 4 · 2017-08-22 14:33:38

1.1k

Views

Local flow of a vector field, local one-parameter subgroup of diffeomorphism group?

Published on 22 Aug 2017 - 14:33

score 310 · Answer 5 · 2026-03-25 16:03:30

310

Views

Mono(epi)morphisms as im(sub)mersions in the category of manifolds

Published on 25 Mar 2026 - 16:03

score 759 · Answer 6 · 2017-09-14 21:33:59

759

Views

Prove $f$ is a local diffeomorphism

Published on 14 Sep 2017 - 21:33

score 137 · Answer 7 · 2017-09-20 02:55:28

137

Views

Prove that $F$ is a diffeomorphism.

Published on 20 Sep 2017 - 2:55

score 339 · Answer 8 · 2017-10-21 14:20:20

339

Views

Prove that a manifold given by a system of equations in $\mathbb{R}^4$ is diffeomorphic to the 2-torus $T^2$

Published on 21 Oct 2017 - 14:20

score 783 · Answer 9 · 2017-11-05 16:29:50

783

Views

Inverse function theorem local injectivity proof

Published on 05 Nov 2017 - 16:29

score 106 · Answer 10 · 2026-03-25 09:27:05

106

Views

Fractional Sobolev space on Union of Sets

Published on 25 Mar 2026 - 9:27

score 149 · Answer 11 · 2026-03-25 13:04:41

149

Views

Diffeomorphisms and their derivatives

Published on 25 Mar 2026 - 13:04

score 1.4k · Answer 12 · 2017-11-21 11:15:33

1.4k

Views

How can I prove that a cylinder is diffeomorphic to a twice-punctured $n$-sphere?

Published on 21 Nov 2017 - 11:15

score 51 · Answer 13 · 2017-11-24 07:33:20

51

Views

Show that ($|F (A)| = |A|$ for every measurable $A \subseteq U$) $\iff$ ($|$det $dF (x)| = 1$ ∀x ∈ U$)

Published on 24 Nov 2017 - 7:33

score 122 · Answer 14 · 2017-12-01 11:16:54

122

Views

$\mathbb{R}^{n+1}\setminus\{0\}\rightarrow S^n$ is a submersion

Published on 01 Dec 2017 - 11:16

score 196 · Answer 15 · 2017-12-04 08:20:08

196

Views

Example of a diffeomorphism $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ such that the image of an annulus is a bigger annulus.

Published on 04 Dec 2017 - 8:20

List Question

A possible geometric inequality on Jacobian integrals of diffeomorphisms

The canonical projection $\mathbb{S}^n\twoheadrightarrow\mathbb{R}P^n$ is a local diffeomorphism.

Can diffeomorphisms only be defined on real manifolds?

Local flow of a vector field, local one-parameter subgroup of diffeomorphism group?

Mono(epi)morphisms as im(sub)mersions in the category of manifolds

Prove $f$ is a local diffeomorphism

Prove that $F$ is a diffeomorphism.

Prove that a manifold given by a system of equations in $\mathbb{R}^4$ is diffeomorphic to the 2-torus $T^2$

Inverse function theorem local injectivity proof

Fractional Sobolev space on Union of Sets

Diffeomorphisms and their derivatives

How can I prove that a cylinder is diffeomorphic to a twice-punctured $n$-sphere?

Show that ($|F (A)| = |A|$ for every measurable $A \subseteq U$) $\iff$ ($|$det $dF (x)| = 1$ ∀x ∈ U$)

$\mathbb{R}^{n+1}\setminus\{0\}\rightarrow S^n$ is a submersion

Example of a diffeomorphism $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ such that the image of an annulus is a bigger annulus.

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