The normalized curve shortening flow and homothetic solutions
The authors investigate the curve shortening flow; i.e. the evolution of a regular closed curve \(\gamma\) in the plane according to the equation \(\partial \gamma /\partial t=kN\) where k is the curvature and N the normal of \(\gamma\). First they modify the flow such that the curves maintain constant speed but are geometrically the same. Then they classify curves that evolve through homothetic curves. Furthermore they prove convergence and divergence results for the flow and compare these with the homothetic solutions.
scientific article; zbMATH DE number 3951450