Question

If $\phi : \partial{M} \times [0,1) \to M $ is an embedding prove that $\phi(\partial{M} \times [0,a])$ is closed in $M$.

score 30 · Answer 1 · 2026-03-25 12:27:07

30

Views

If $\phi : \partial{M} \times [0,1) \to M $ is an embedding prove that $\phi(\partial{M} \times [0,a])$ is closed in $M$.

Published on 25 Mar 2026 - 12:27

score 138 · Answer 2 · 2020-09-20 06:38:23

138

Views

Divergence of a smooth map $M\to\mathbb R^d$ on a submanifold $M$ of $\mathbb R^d$ with boundary

Published on 20 Sep 2020 - 6:38

score 109 · Answer 3 · 2020-09-20 11:34:38

109

Views

Does $(\operatorname{div}fX)(a)=\langle\nabla f(a),X(a)\rangle+f(a)(\text{div}X)(a)$ hold for a scalar field $f$ and vector field $M$ on a manifold?

Published on 20 Sep 2020 - 11:34

score 56 · Answer 4 · 2020-09-22 04:56:32

56

Views

Gram determinant of a boundary chart of a submanifold

Published on 22 Sep 2020 - 4:56

score 104 · Answer 5 · 2026-02-23 08:30:36

104

Views

Build manifold based on boundary information

Published on 23 Feb 2026 - 8:30

score 27 · Answer 6 · 2020-09-24 15:51:55

27

Views

partial integration on the boundary of a submanifold

Published on 24 Sep 2020 - 15:51

score 306 · Answer 7 · 2020-09-25 14:00:16

306

Views

Smoothly extending a metric from a manifold with boundary to an attached cylinder

Published on 25 Sep 2020 - 14:00

score 86 · Answer 8 · 2026-03-26 23:10:55

86

Views

"Unitary" extension of the normal field from the boundary of a manifold

Published on 26 Mar 2026 - 23:10

score 25 · Answer 9 · 2020-09-26 10:07:20

25

Views

Bordism and regular values of a distance map

Published on 26 Sep 2020 - 10:07

score 61 · Answer 10 · 2020-09-26 15:27:38

61

Views

Can we show that this boundary integral functional is continuous?

Published on 26 Sep 2020 - 15:27

score 75 · Answer 11 · 2026-03-27 14:03:19

75

Views

If there is a diffeomorphism from an open subset of $\mathbb R^d$ onto a submanifold $M$ of $\mathbb R^d$, then $M$ is open

Published on 27 Mar 2026 - 14:03

score 92 · Answer 12 · 2026-03-25 20:42:02

92

Views

Why is this application of the chain rule for the pushforward well-defined?

Published on 25 Mar 2026 - 20:42

score 434 · Answer 13 · 2026-03-26 19:01:57

434

Views

Is the restriction of a diffeomorphism to a manifold $M$ an open map from $M$ to $M$?

Published on 26 Mar 2026 - 19:01

score 584 · Answer 14 · 2020-10-02 17:41:08

584

Views

Proving sufficient conditions for immersed submanifolds to be embedded

Published on 02 Oct 2020 - 17:41

score 93 · Answer 15 · 2020-10-04 16:01:07

93

Views

If $T_t$ is a flow and $M$ is a manifold with $T_t(\partial M)⊆\partial M$ for all $t$, we've already got $T_t(\partial M)=\partial M$ for all $t$

Published on 04 Oct 2020 - 16:01

List Question

If $\phi : \partial{M} \times [0,1) \to M $ is an embedding prove that $\phi(\partial{M} \times [0,a])$ is closed in $M$.

Divergence of a smooth map $M\to\mathbb R^d$ on a submanifold $M$ of $\mathbb R^d$ with boundary

Does $(\operatorname{div}fX)(a)=\langle\nabla f(a),X(a)\rangle+f(a)(\text{div}X)(a)$ hold for a scalar field $f$ and vector field $M$ on a manifold?

Gram determinant of a boundary chart of a submanifold

Build manifold based on boundary information

partial integration on the boundary of a submanifold

Smoothly extending a metric from a manifold with boundary to an attached cylinder

"Unitary" extension of the normal field from the boundary of a manifold

Bordism and regular values of a distance map

Can we show that this boundary integral functional is continuous?

If there is a diffeomorphism from an open subset of $\mathbb R^d$ onto a submanifold $M$ of $\mathbb R^d$, then $M$ is open

Why is this application of the chain rule for the pushforward well-defined?

Is the restriction of a diffeomorphism to a manifold $M$ an open map from $M$ to $M$?

Proving sufficient conditions for immersed submanifolds to be embedded

If $T_t$ is a flow and $M$ is a manifold with $T_t(\partial M)⊆\partial M$ for all $t$, we've already got $T_t(\partial M)=\partial M$ for all $t$

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