Question

If $T$ is a continuous bijection on $\mathbb R^d$, and $M$ is a $C^1$-submanifold with boundary, is $T(\partial M)=\partial T(M)$?

score 61 · Answer 1 · 2020-07-16 10:09:03

61

Views

If $T$ is a continuous bijection on $\mathbb R^d$, and $M$ is a $C^1$-submanifold with boundary, is $T(\partial M)=\partial T(M)$?

Published on 16 Jul 2020 - 10:09

score 64 · Answer 2 · 2020-07-18 09:54:36

64

Views

A simple shape derivative example

Published on 18 Jul 2020 - 9:54

score 72 · Answer 3 · 2026-03-25 19:05:45

72

Views

boundary and interior of an embedded submanifold with boundary described by a single chart

Published on 25 Mar 2026 - 19:05

score 83 · Answer 4 · 2020-07-20 18:40:13

83

Views

Shape derivative of a boundary integral with a continuously differentiable function on a "tubular neighborhood"

Published on 20 Jul 2020 - 18:40

score 575 · Answer 5 · 2020-07-21 14:55:18

575

Views

Definition and intuition of a tubular neighborhood of a submanifold

Published on 21 Jul 2020 - 14:55

score 149 · Answer 6 · 2026-03-25 11:13:17

149

Views

The Transverality Theorem in Differentiable Topology by Guillemin and Pollack

Published on 25 Mar 2026 - 11:13

score 167 · Answer 7 · 2020-07-30 00:40:17

167

Views

What can we say if the gradient at the boundary has constant norm?

Published on 30 Jul 2020 - 0:40

score 434 · Answer 8 · 2026-03-25 01:27:09

434

Views

If the boundary of an open connected set $\Omega$ of class $C^1$ is bounded $\Rightarrow$ $\Omega$ is bounded?

Published on 25 Mar 2026 - 1:27

score 106 · Answer 9 · 2026-03-25 03:25:35

106

Views

Munkres Problem: Define a $C^{\infty}$ map $f: \mathbb{R}^9 \to \mathbb{R}^6$ such that $O(3)$ is the solution of $f(x)=0$.

Published on 25 Mar 2026 - 3:25

score 1.1k · Answer 10 · 2026-03-25 04:11:45

1.1k

Views

If a continuous function is locally injective and injective on the boundary, is it injective?

Published on 25 Mar 2026 - 4:11

score 296 · Answer 11 · 2026-03-24 21:49:45

296

Views

Smoothness of the boundary is the only obstruction for being a submanifold with boundary?

Published on 24 Mar 2026 - 21:49

score 237 · Answer 12 · 2026-03-25 15:42:24

237

Views

When is a continuous map $f: M \longrightarrow N$ between smooth manifolds homotopic to a smooth one?

Published on 25 Mar 2026 - 15:42

score 221 · Answer 13 · 2026-03-25 02:34:46

221

Views

Manifolds with corners

Published on 25 Mar 2026 - 2:34

score 86 · Answer 14 · 2026-03-26 06:19:12

86

Views

$T_P(M)$ vs. $T_P(\partial M)$

Published on 26 Mar 2026 - 6:19

score 741 · Answer 15 · 2026-03-24 22:03:23

741

Views

Are topological manifolds with boundary metrizable?

Published on 24 Mar 2026 - 22:03

List Question

If $T$ is a continuous bijection on $\mathbb R^d$, and $M$ is a $C^1$-submanifold with boundary, is $T(\partial M)=\partial T(M)$?

A simple shape derivative example

boundary and interior of an embedded submanifold with boundary described by a single chart

Shape derivative of a boundary integral with a continuously differentiable function on a "tubular neighborhood"

Definition and intuition of a tubular neighborhood of a submanifold

The Transverality Theorem in Differentiable Topology by Guillemin and Pollack

What can we say if the gradient at the boundary has constant norm?

If the boundary of an open connected set $\Omega$ of class $C^1$ is bounded $\Rightarrow$ $\Omega$ is bounded?

Munkres Problem: Define a $C^{\infty}$ map $f: \mathbb{R}^9 \to \mathbb{R}^6$ such that $O(3)$ is the solution of $f(x)=0$.

If a continuous function is locally injective and injective on the boundary, is it injective?

Smoothness of the boundary is the only obstruction for being a submanifold with boundary?

When is a continuous map $f: M \longrightarrow N$ between smooth manifolds homotopic to a smooth one?

Manifolds with corners

$T_P(M)$ vs. $T_P(\partial M)$

Are topological manifolds with boundary metrizable?

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