The compression theorem I.

Rourke, Colin; Sanderson, Brian

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We introduce a skeletal structure $(M, U)$ in $ℝ^{n + 1}$ , which is an $n$ - dimensional Whitney stratified set $M$ on which is defined a multivalued “radial vector field” $U$ . This is an extension of notion of the Blum medial axis of a region in $ℝ^{n + 1}$ with generic smooth boundary. For such a skeletal structure there is defined an “associated boundary” $ℬ$ . We introduce geometric invariants of the radial vector field $U$ on $M$ and a “radial flow” from $M$ to $ℬ$ . Together these allow us to provide sufficient numerical conditions...

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