- #1

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Its volume distortion is defined as $G=det(D

_{f}

^{t}D

_{f}).$ If $n=1$, one can deduce that $G=1+|\nabla f|^2$.

What happens for $n>1$? Can one bound from below this $G$? If so: under which assumptions?

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- Thread starter eyenir
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- #1

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Its volume distortion is defined as $G=det(D

What happens for $n>1$? Can one bound from below this $G$? If so: under which assumptions?

- #2

wrobel

Science Advisor

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did not you know that the image of a compact set under a continuous mapping is a compact set?Let $U$ be a compact set in $\mathbb{R}^k$ and let $f:U\to\mathbb{R}^n$ be a $C^1$ bijection.

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