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Centre for Geometric Analysis Seminar Series
June 13 @ 10:30 am - 11:30 am
Dr Philip Schrader (UWA)
Gradient flows of length
The classical curve shortening flow is a length gradient flow which evolves planar curves in the (negative) normal direction proportional to curvature. To define a gradient flow of the length requires a Riemannian metric on the space of curves and in the case of the curve shortening flow the metric is an invariant L^2 metric. The space of curves being infinite dimensional, not all Riemmanian metrics are equivalent, and in fact it was proved by Michor and Mumford that the L^2 metric gives a trivial distance. In this talk I will explain Michor and Mumford’s proof, and present some results from investigating the length gradient flow associated with an H^1 metric on the space of curves (joint work with G. Wheeler and V.M. Wheeler).