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1
vote
1answer
43 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
votes
0answers
153 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 ...
10
votes
2answers
402 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] ...
11
votes
1answer
555 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?
17
votes
1answer
884 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 ...