The smoothing-theory tag has no usage guidance.

**2**

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### Cubic splines convergence?

I am looking for a basic, classical, result on approximating a smooth function using cubic and linear splines. Is there a reference on the convergence, in some sense, of the splines to the function of ...

**1**

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**1**answer

64 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 $\...

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173 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 ...

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**2**answers

792 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**

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**1**answer

621 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?

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984 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 ...