Pure Maths Colloquium: Minima of the Euler functional for plane curves
25 April 2016 16:00 in CM221
The Euler functional of a smooth plane curve is the integral along the curve of the square of its curvature. In 1774, Euler posed the problem of finding the curves that give the minima of his functional. In the talk, we will give the answer to this problem, sketch its proof, show that it implies the Whitney-Graustein theorem on the classification of regular plane curves up to regular homotopy, and run computer animations showing the gradient descent of curves to their minimal form. The talk is based on joint work with Oleg Karpenkov (Liverpool) and Sergei Avvakumov (Vienna).
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