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Results tagged with geometric-measure-theory
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user 13093
Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.
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Integral of the square of the areas of slices of a shape
Suppose $\omega$ is a bounded shape in $\Bbb{R}^3$ and that $\{z : (x,y,z) \in \omega \}=[0,T]$ (that is, the shape is exactly contained in the band $\{z \in [0,T]\}$. If we denote by $\omega_t = \{(x …
- 9,007
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Convergent algorithm for dividing a body into two regions of equal volume
There is an algorithm, based on a $\Gamma$-convergence result, which can find the minimal surface which divides a shape into two regions of equal volume. More details can be found in this link and thi …
- 2,222