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Results tagged with geometric-measure-theory
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user 109533
Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.
5
votes
Mass minimizing current in real homology class
Since $T$ is a closed current, it has a local primitive $u$, which is a function such that for any smooth $n - 1$-form $\varphi$ with support on the set where $u$ is defined,
$$\int_T \varphi = \int_M …
- 708
2
votes
Accepted
Are smooth surfaces embedded in R3 , with finite area, always the boundary of a finite perim...
Your question is worded a bit confusingly, in particular I can't tell if you want compactness or not.
If you don't want compactness, it's not entirely clear what you mean by "bounding": take the unit …
- 708
3
votes
Accepted
Is every area-minimizing cone a level set of a least-gradient function?
Yes. Let $L := \mathbf C \cap \partial B_1$ be the link of $\mathbf C$. Since $\mathbf C$ meets $\partial B_1$ transversely and is smooth near $\partial B_1$, $L$ can be viewed as a closed submanifold …
- 708
3
votes
Mass of the push forward of a k-current with fixed orientation
Your assumption that $T$ has direction $e^1 \wedge e^2$ means that for some distribution $u$, $T = u e^1 \wedge e^2$ (actually, since $T$ has finite mass, $u$ is a Radon measure). We're trying to comp …
- 708