Mathematical Sciences: Studies in Geometric Analysis and Algebra

这一建议是为了研究几何演化过程，如可能模拟晶体从熔体开始冻结的枝晶生长。在几何测量理论中，晶体是有限周长的集合，温度场和浓度场是属于适当Sobolev空间的函数。最后的演化是离散时间近似的极限，其中晶体的几何形状是通过求解变分问题来确定的，而场是通过扩散方程来演化的。

This proposal is for investigation of geometric evolution processes such as might model dendritic growth of a crystal freezing from its melt. The mathematical setting is that of geometric measure theory in which crystals are sets of finite perimeter and temperature and concentration fields are functions belonging to appropriate Sobolev spaces. The final evolution is a limit of discrete time approximations in which crystal geometries are determined by solving variational problems and fields evolve by diffusion equations.