Question

Let $f:\mathbb{R}^n\rightarrow \mathbb{R}^n$ be continuously differentiable. $\forall x,y\in \mathbb{R}^n$, $d\big(f(x),f(y)\big)\geq a\cdot d(x,y)$

score 174 · Answer 1 · 2021-03-25 14:21:13

174

Views

Let $f:\mathbb{R}^n\rightarrow \mathbb{R}^n$ be continuously differentiable. $\forall x,y\in \mathbb{R}^n$, $d\big(f(x),f(y)\big)\geq a\cdot d(x,y)$

Published on 25 Mar 2021 - 14:21

score 744 · Answer 2 · 2021-03-26 00:31:52

744

Views

$\mathbb{CP}^1$ is diffeomorphic to $S^2$.

Published on 26 Mar 2021 - 0:31

score 94 · Answer 3 · 2021-03-26 22:31:21

94

Views

A linear combination of diffeomorphims still a diffeomorphism?

Published on 26 Mar 2021 - 22:31

score 271 · Answer 4 · 2021-03-31 14:33:22

271

Views

Showing an isometry preserves angles

Published on 31 Mar 2021 - 14:33

score 68 · Answer 5 · 2021-04-01 04:29:58

68

Views

Book recommendation: Constructing diffeomorphisms / homeomorphisms (elementary differential geometry)

Published on 01 Apr 2021 - 4:29

score 161 · Answer 6 · 2021-04-04 20:55:44

161

Views

subspace topology and universal property

Published on 04 Apr 2021 - 20:55

score 360 · Answer 7 · 2021-04-05 22:58:58

360

Views

Smooth invariance of domain and diffeomorphisms

Published on 05 Apr 2021 - 22:58

score 79 · Answer 8 · 2021-04-06 16:34:21

79

Views

the "simplest" spherical metric of an arbitrary Riemannian 3-manifold diffeomorphic to $\mathbb{R}^3$

Published on 06 Apr 2021 - 16:34

score 230 · Answer 9 · 2021-04-09 12:18:38

230

Views

Prove that $\frac{rx}{\sqrt{r^2-|x|^2}}$ is a diffeomorphism

Published on 09 Apr 2021 - 12:18

score 115 · Answer 10 · 2026-03-26 15:07:23

115

Views

Application of the inverse function theorem on a convex set

Published on 26 Mar 2026 - 15:07

score 211 · Answer 11 · 2021-04-11 14:31:20

211

Views

Every point $p\in\ M$ has an open neighborhood $U \subset M$ which is diffeomorphic to $R^n$

Published on 11 Apr 2021 - 14:31

score 53 · Answer 12 · 2021-04-12 14:04:08

53

Views

Cartesian product of diffeomorphic Lie groups

Published on 12 Apr 2021 - 14:04

score 60 · Answer 13 · 2021-04-18 18:09:00

60

Views

Building diffeomorphism

Published on 18 Apr 2021 - 18:09

score 517 · Answer 14 · 2021-04-20 22:04:27

517

Views

Alternatives to the classical pendulum ODE

Published on 20 Apr 2021 - 22:04

score 60 · Answer 15 · 2021-04-21 07:26:21

60

Views

Relation between $\rm{Diff}(\mathbb{R}^n) \times \rm{Diff}(\mathbb{R}^m)$ and $\rm{Diff}(\mathbb{R}^n \times \mathbb{R}^m)$

Published on 21 Apr 2021 - 7:26

List Question

Let $f:\mathbb{R}^n\rightarrow \mathbb{R}^n$ be continuously differentiable. $\forall x,y\in \mathbb{R}^n$, $d\big(f(x),f(y)\big)\geq a\cdot d(x,y)$

$\mathbb{CP}^1$ is diffeomorphic to $S^2$.

A linear combination of diffeomorphims still a diffeomorphism?

Showing an isometry preserves angles

Book recommendation: Constructing diffeomorphisms / homeomorphisms (elementary differential geometry)

subspace topology and universal property

Smooth invariance of domain and diffeomorphisms

the "simplest" spherical metric of an arbitrary Riemannian 3-manifold diffeomorphic to $\mathbb{R}^3$

Prove that $\frac{rx}{\sqrt{r^2-|x|^2}}$ is a diffeomorphism

Application of the inverse function theorem on a convex set

Every point $p\in\ M$ has an open neighborhood $U \subset M$ which is diffeomorphic to $R^n$

Cartesian product of diffeomorphic Lie groups

Building diffeomorphism

Alternatives to the classical pendulum ODE

Relation between $\rm{Diff}(\mathbb{R}^n) \times \rm{Diff}(\mathbb{R}^m)$ and $\rm{Diff}(\mathbb{R}^n \times \mathbb{R}^m)$

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