The isoperimetric dimension of M is the supremum of all values of d such that M satisfies a d-dimensional isoperimetric inequality.
Read more about Isoperimetric Dimension: Examples, Isoperimetric Dimension of Graphs, Consequences of Isoperimetry
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“God cannot be seen: he is too bright for sight; nor grasped: he is too pure for touch; nor measured: for he is beyond all sense, infinite, measureless, his dimension known to himself alone.”
—Marcus Minucius Felix (2nd or 3rd cen. A.D.)