Global Curvature for Rectifiable Loops
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On rectifiable curves with Lp-bounds on global curvature: self-avoidance, regularity, and minimizing knots
We discuss the analytic properties of curves γ whose global curvature function ρG[γ ]−1 is p-integrable. It turns out that theLp-norm Up(γ ) := ‖ρG[γ ]−1‖Lp is an appropriate model for a self-avoidance energy interpolating between “soft” knot energies in form of singular repulsive potentials and “hard” self-obstacles, such as a lower bound on the global radius of curvature introduced by Gonzale...
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