7 gives a computed non-uniqueness result. 8 shows how to combine level set and Fast Marching ideas to build stable algorithms for computing flow under the second derivative of curvature. 9,10,11, and 12 are theoretical results built using these level set ideas. Movie of the above curve collapsing General explanations, movies, simulations, java applets and details about geometric flow. In many physical problems, interfaces move with a speed that depends on the local curvature.
Some common examples are flame propagation, crystal growth, and oil-water boundaries.
We idealize the front as a closed, non-intersecting, initial hypersurface flowing along its gradient field with a speed that depends on the curvature. Because explicit solutions seldom exist, numerical approximations are often used. In this paper, we review some recent work on algorithms for attacking these problems. We show that algorithms based on direct parameterizations of the moving front face considerable difficulties. This is because such algorithms adhere to local properties of the solution, rather than the global structure.