List questions from manifolds-with-boundary

49

Views

If $v(t,x)\in T_x\:\partial M$ for all $(t,x)\in[0,\tau]\times\partial M$, then $f(x)(\text{div}_{\partial M}v_0)(x)+⟨\nabla f(x),v_0(x)⟩=0$

Published on 05 Oct 2020 - 10:14

40

Views

Does the pushforward $T_a(X)$ of a vector field $X$ on $M$ map to $T_a(X)$ again?

Published on 27 Mar 2026 - 4:58

445

Views

Smooth Jordan-Schönflies Curve Theorem

Published on 06 Oct 2020 - 14:16

81

Views

Jordan-Schönflies Curve Theorem - Multiple Curves

Published on 06 Oct 2020 - 15:38

61

Views

Curvature of a local deformation of a Riemannian manifold

Published on 26 Mar 2026 - 19:12

67

Views

Quotient space of $\{\theta\in\mathcal D(\mathbb R^d,\mathbb R^d):\langle\theta(x),\nu_{∂Ω}(x)\rangle=0\text{ for all }x\in ∂Ω\}$

Published on 10 Oct 2020 - 15:25

114

Views

Can we form a topological or Banach space of $C^1$-differentiable functions on a manifold?

Published on 25 Mar 2026 - 20:36

47

Views

Cover the closed ball, treated as a submanifold with boundary, with two charts

Published on 13 Oct 2020 - 10:17

52

Views

Smooth functions defined on connected sums

Published on 26 Mar 2026 - 4:29

154

Views

Perturbing a Riemannian metric near the boundary to a product-type metric

Published on 18 Oct 2020 - 8:51

308

Views

Some examples and non-examples of topological manifolds (w boundary or not)

Published on 19 Oct 2020 - 16:57

38

Views

Are Lipchitz isometries smooth up to the boundary?

Published on 21 Oct 2020 - 5:11

34

Views

Find $X$ such that $\partial X = S^1 \times T$

Published on 26 Oct 2020 - 16:29

92

Views

A topological manifold whose boundary is $S^1 \lor S^1$

Published on 26 Oct 2020 - 16:45

114

Views

Usefulness of compact boundary proving uniqueness in gluing smooth manifolds

Published on 10 Nov 2020 - 9:18

List Question

If $v(t,x)\in T_x\:\partial M$ for all $(t,x)\in[0,\tau]\times\partial M$, then $f(x)(\text{div}_{\partial M}v_0)(x)+⟨\nabla f(x),v_0(x)⟩=0$

Does the pushforward $T_a(X)$ of a vector field $X$ on $M$ map to $T_a(X)$ again?

Smooth Jordan-Schönflies Curve Theorem

Jordan-Schönflies Curve Theorem - Multiple Curves

Curvature of a local deformation of a Riemannian manifold

Quotient space of $\{\theta\in\mathcal D(\mathbb R^d,\mathbb R^d):\langle\theta(x),\nu_{∂Ω}(x)\rangle=0\text{ for all }x\in ∂Ω\}$

Can we form a topological or Banach space of $C^1$-differentiable functions on a manifold?

Cover the closed ball, treated as a submanifold with boundary, with two charts

Smooth functions defined on connected sums

Perturbing a Riemannian metric near the boundary to a product-type metric

Some examples and non-examples of topological manifolds (w boundary or not)

Are Lipchitz isometries smooth up to the boundary?

Find $X$ such that $\partial X = S^1 \times T$

A topological manifold whose boundary is $S^1 \lor S^1$

Usefulness of compact boundary proving uniqueness in gluing smooth manifolds

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