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6
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1
answer
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Can we approximate a vector field on the plane with non-vanishing vector fields in $W^{1,2}$?
Let $V$ be a compactly-supported vector field on $\mathbb{R}^2$, whose zeros inside some open neighbourhood of the closed unit disk $\mathbb{D}^2$ are isolated.
Does there exist a sequence of ...
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8
votes
1
answer
599
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Can we perturb a map $\mathbb{R}^n \to \mathbb{R}^n$ to have distinct singular values?
$\newcommand{\SO}[1]{\text{SO}(#1)}$
$\newcommand{\dist}{\operatorname{dist}}$
Let $\mathbb{D}^n$ be the closed $n$-dimensional unit ball, and let $f:\mathbb{D}^n \to \mathbb{R}^n$ be smooth.
Set
$$...
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