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- W4320342387 abstract "In this article, we solve the relative isoperimetric problem in $[0,1]^3$ for subsets whose boundaries are in the union of a finite number of coordinate-parallel hyperplanes. Up to isometries of the cube or sets of measure $0$, the minimizers are of the form $[0,epsilon]^3$, $[0,epsilon]^2 times [0,1]$, or $[0,epsilon] times [0,1]^2$ for some $epsilon > 0$. This should be compared to the conjectured minimizers for the unconstrained relative isoperimetric problem in $[0,1]^3$, which are (up to isometries and sets of measure $0$) of the form $left( B^3(epsilon) right) cap [0,1]^3$, $left( B^2(epsilon) times [0,1] right) cap [0,1]^3$, or $[0,epsilon] times [0,1]^2$ for some $epsilon > 0$. Here, $B^k(epsilon)$ is the closed ball in $mathbb{R}^k$ of radius $epsilon$ centered at the origin." @default.
- W4320342387 created "2023-02-13" @default.
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- W4320342387 date "2023-02-08" @default.
- W4320342387 modified "2023-09-23" @default.
- W4320342387 title "On the relative isoperimetric problem for the cube" @default.
- W4320342387 doi "https://doi.org/10.48550/arxiv.2302.04382" @default.
- W4320342387 hasPublicationYear "2023" @default.
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