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Results tagged with geometric-measure-theory
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user 62739
Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.
5
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1
answer
460
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Is every set with finite $\mathcal{H}^{n-1}$ measure a set of locally finite perimeter?
Given a measurable set $E \subset \mathbb{R}^d$, with $\mathcal{H}^{d-1} (\partial E) < +\infty$, is it true in general that $E$ is a set of locally finite perimeter? that is, is it true that $\int_B …
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0
votes
0
answers
22
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A general rule for approximating the perimeter of a set with finite perimeter in terms of th...
I want to know if it is possible to have a general rule for approximating the perimeter of a set $E\subset \mathbb{R}^n$ with finite perimeter in terms of the volume (Lebesgue measure) of a sequence o …
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2
votes
0
answers
156
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What is the boundary of the set $\{ x : dist (x ,\partial \Omega) > \alpha \}$ for a domain ...
Let $\Omega$ is a bounded open domain in $\mathbb R ^n$, and $\alpha \geq 0$ a real number, and consider the set $ E_\alpha = \{ x \in \Omega : \text{dist}(x , \partial \Omega) > \alpha\} $, which $\ …
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3
votes
1
answer
371
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Hausdorff measure of intersection of a ball and a set in $\mathbb {R} ^ n$
Let $A$ a subset of $\mathbb R ^n$, $B=B(x,r) \subset \mathbb {R} ^n$ an open ball, and denote the $(n-1)$-dimensional Hausdorff measure in $\mathbb R ^n$ by $\mathcal H^{n-1}$. Also assume that $\ma …
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1
vote
Origin of term Ahlfors-David regular
As I know the second inequality in the definition is due to Ahlfors, and the first one is due to Guy David. Let $E$ be a subset of $\mathbb {R} ^ n $. One says that $E$ is Ahlfors-David regular of ord …
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