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3 votes
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Shrinking a disk with fixed differential

Here are a few comments that you might find useful, though they don't completely solve the problem. First, using symmetries of the problem, you can easily reduce to the case that $f$ is mapping the …
Robert Bryant's user avatar
20 votes
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Are all maps $\mathbb{R}^2 \to \mathbb{R}^2$ with fixed singular values affine?

Answer modified on 1 February 2020: It's not true 'locally' in the sense that non-affine $f$'s satisfying this system of PDE can be constructed on some open sets in $\mathbb{R}^2$. This first order …
Robert Bryant's user avatar