3. Geometric curve shortening flow

3.1 What kind of equations for curve smoothing? 3.1.1 Invariant flows3.1.2 Symmetry group of flow3.2 Differential invariants 3.2.1 General form of invariant flows3.2.2 The mean curvature flow is the Euclidean intrinsic heat flow3.2.3 The affine invariant flow: the simplest affine invariant curve flow3.3 General properties of second order parabolic flows: a digest 3.3.1 Existence and uniqueness for mean curvature and affine flows3.3.2 Short-time existence in the general case3.3.3 Evolution of convex curves3.3.4 Evolution of the length3.3.5 Evolution of the area3.4 Smoothing staircases3.5 Bibliographical notes