3. Geometric curve shortening flow

3.1.1 Invariant flows

3.1.2 Symmetry group of flow

3.2.1 General form of invariant flows

3.2.2 The mean curvature flow is the Euclidean intrinsic heat flow

3.2.3 The affine invariant flow: the simplest affine invariant curve flow

3.3.1 Existence and uniqueness for mean curvature and affine flows

3.3.2 Short-time existence in the general case

3.3.3 Evolution of convex curves

3.3.4 Evolution of the length

3.3.5 Evolution of the area