Evolving plane curves by curvature in relative geometries. II (Q1341290)

[Part I, cf. ibid. 72, No. 2, 441-466 (1993; Zbl 0798.53041).] The existence of self-similar solutions to the anisotropic curve shortening equation is proved: Theorem. Given any positive \(C^ 2\) function \(\gamma\) on \(S^ 1\) there exists a solution to the equation \({\partial X \over \partial t} = \gamma(\theta) kN\), which is self- similar. This means that the evolution shrinks the initial curve without changing its shape.