# Questions tagged [geometric-measure-theory]

The study of the geometric structure of measures, as well as the study of geometry from a measure-theoretic viewpoint, geometric measure theory has applications in partial differential equations, harmonic analysis, differential geometry, Riemannian geomerty, sub-Riemannian geometry, as well as calculus of variations. Statements such as the isoperimetric inequality and the coarea formula, and subjects such as the Plateau problem belong under this tag.

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### Riesz's representation of a k-current

Reading "Introduction to GMT" by Simon, at page 136 he says that thanks to Riesz's representation theorem we can view k-currents ar Radon measures, or to be more precise he says that given a ...
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### regular analytic 1-dim. foliation of $M=(0,1)^3$

I'm investigating this question: Does there exist a regular analytic $1-$dim. foliation of $M=(0,1)^3$ s.t. all leaves include both $(0,1,1)$ and $(1,0,0)$ or approach these points in the limit? I ...
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### What does a hashtag subscript mean?

I've been coming accross notation like this $\gamma = (id,id)_\# \mu$, where the hashtag/pound sign is used in the subscript. From context, it seems to have something to do with marginalizing ...
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### Function with harmonic properties

Let $g(z)$ be a continuous function on $\mathbb R^n\setminus \{0\}$. $$\int_{B_R(0)} |g(z)| dz \leq C_1$$ for some constant $C_1$, and with $B_R (0)$ being the ball of radius $R$ centered at the ...
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### Almgren and Taylor's movie about soap bubbles

As I know, in 1970's two well-known geometric analysts, Fred Almgren and Jean Taylor, along with mathematician Michele Emmer, produced a film about minimal surfaces entitled "Soap Bubbles". ...