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Smoothness and geometry of boundaries associated to skeletal structures I: sufficient conditions for smoothness

2003; Association of the Annals of the Fourier Institute; Volume: 53; Issue: 6 Linguagem: Inglês

10.5802/aif.1997

1777-5310

James Damon,

Mathematical Dynamics and Fractals

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 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.