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Consider $\mathbb{R}_t \times \mathbb{R}_x ^n$ , let $b_1(t,x)$ and $b_2 (t,x)$ be two velocity fields with all the regularity you want and consider the flow of the point $(0,x_0)$ for a time $T$. No …

In the article "Funzioni BV e tracce" by Anzellotti and Giaquinta (MR555952, Zbl 0432.46031), at page 6 you can read (assume $\Omega \subset \mathbb{R}^n$ open): "The following example shows that the …

I am currently studying GMT and a topic that has popped up in the course is the use of calibrations as a tool for proving that a particular set $E$ attains the minimum for the problem $$min \left \lbr …

Given a set $A \subset \mathbb{R}^n$, this is called d-rectifiable if it can be covered by a countable union of images of lipshitz functions from $\mathbb{R}^d $ to $ \mathbb{R}^n $ and a $\mathcal{H} …

This is probably a simple question, maybe more suited for MSE. In the coarea formula, you have $$\int_{{\mathbb{R}}^n} g (x) |\nabla f(x)|\, dx= \int_\mathbb{R} \left(\int_{\{f=t\}} g d \mathcal{H}^{n …

$\DeclareMathOperator{\Mass}{Mass}$Let $f: \mathbb{R}^n \to \mathbb{R}^n$ be a smoth map. Given a $2$-vector (in general a $k$-vector but let's stick to $2$) $v_1 \wedge v_2 \in \Lambda_2 (\mathbb{R} …