Let $U$ be a compact set in $\mathbb{R}^k$ and let $f:U\to\mathbb{R}^n$ be a $C^1$ bijection. Consider the manifold $M=f(U)$.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Bounding the volume distortion of a manifold

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**