Nonlinear functionals that appear as a product of two integrals are considered in the context of elastic curves of variable length. A technique is introduced that exploits the fact that one of the… (More)

This paper considers the negative gradient trajectories associated with the modified total squared curvature functional k 2 + ν ds. The focus is on the limiting behavior as ν tends to zero from the… (More)

A method to generate periodic geodesics in arbitrary level surfaces is presented. The underlying algorithm resolves several technical complications posed by the constraints to stay in the surface and… (More)

The traditional techniques of approximation theory in the form of kernel interpolation and cubic spline approximation are used to obtain representations and estimates for functions implicitly defined… (More)

Recent computational breakthroughs in infinite-dimensional optimization have produced explicit, as well as numerically advantageous, gradient formulas. By following the negative gradient… (More)

Assume the curves xτ flow according to ( ) / x x τ τ τ ∂ ∂ = Φ . Evolutions that only use local data, such as curve shortening, yield partial differential equations. In the present paper global… (More)