# Questions tagged [smoothing-theory]

The smoothing-theory tag has no usage guidance.

7
questions

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### Existence of smooth structures on topological $3$-manifolds with boundary

It is said in this thread Unique smooth structure on $3$-manifolds that every topological $3$-manifold admits a smooth structure. However it is not specified whether the manifolds are allowed to have ...

**3**

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**1**answer

136 views

### Smoothing a periodic function of two variables

Let $F \colon \mathbb{R}^2 \to \mathbb{R}^n$ be a $C^{1}$-function 1-periodic in each variable, so it can be considered as a function on the flat torus $\mathbb{T}^2 = \mathbb{R}^2 / \mathbb{Z}^2$. We ...

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**1**answer

122 views

### log-convexity of Mollified function?

Let $f:{\mathbb R}\rightarrow{\mathbb R}_+$ be a log-convex function. Suppose that $f_{\epsilon}$ is the smoothed version of $f$:
$$f_{\epsilon}(x)=\int \varphi_{\epsilon}(x-y)f(y)dy,$$
where $\...

**3**

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**0**answers

195 views

### smoothing a current

Let $M$ be a smooth oriented manifold of dimension $n$ and $T$ a current of dimension $k$ on $M$. Let $\phi:P\times M \to M$ be a proper smooth family of diffeomorphisms of $M$ (i.e. $P$ is a smooth ...

**20**

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**2**answers

2k views

### Isotopy extension theorems

I'm looking for the origins of the isotopy extension theorem in categories other than the smooth category.
Precisely, in the smooth category, the isotopy extension theorem says that if $f : [0,1] \...

**12**

votes

**1**answer

757 views

### Are there non-compact, non-smoothable manifolds?

There do exist manifolds which do not admit any smooth structure at all. But the only examples I've heard of are all compact.
Are there any non-compact, non-smoothable manifolds?

**18**

votes

**1**answer

1k views

### Diffeomorphisms vs homeomorphisms of 3-manifolds

For a smooth 3-manifold $M$, is the natural map from the space of diffeomorphisms of $M$ to the space of homeomorphisms of $M$,
$${\sf Diff}(M) \longrightarrow {\sf Top}(M),$$
a weak homotopy ...