Journal
ANNALES DE L INSTITUT FOURIER
Volume 53, Issue 6, Pages 1941-+Publisher
ANNALES INST FOURIER
DOI: 10.5802/aif.1997
Keywords
skeletal structures; Whitney stratified sets; shock set; radial shape operator; grassfire flow; radial flow
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We introduce a skeletal structure (M, U) in Rn+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 Rn+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 for the smoothness of the boundary B as well as allowing us to determine its geometry. In the course of the proof, we establish the existence of a tubular neighborhood for such a Whitney stratified set.
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