Sobolev--type metrics in the space of curves

A. C. G. Mennucci, A. Yezzi, G. Sundaramoorthi

We define a manifold $M$ where objects $c\in M$ are curves, which we parameterize as $c:S^1\to R^n$ ($n\ge 2$, $S^1$ is the circle). Given a curve $c$, we define the tangent space…