Mathematical Sciences: Weak Solutions of Geometric Evolution Equations

小行星9626405 建议的研究在于黎曼几何的一般领域。更准确地说，它涉及以下几何演化方程：里奇流，平均曲率流，杨米尔斯热流方程。要使用的方法包括几何测量理论，爆破参数，非线性椭圆方程，极小曲面，变分问题的计算机解决方案。 几何演化方程产生于对物理过程的描述，同时从纯几何的观点来看，它们也是有趣的。它们可以用来描述各种热流，长时间流体动力学，以及自然界中随着时间的推移逐渐和连续发生变化的其他现象。

9626405 Ilmanen The proposed research lies in the general area of Riemannian geometry. More precisely, it deals with the following geometric evolution equations: the Ricci flow, mean curvature flow, and Yang-Mills heat flow equations. The methods to be used include geometric measure theory, blowup arguments, nonlinear elliptic equations, minimal surfaces, and computer solutions of variational problems. Geometric evolution equations arise in the description of physical processes, and at the same time they are interesting from a purely geometric standpoint. They can be used to describe various heat flows, long time fluid dynamics, and other phenomena in nature where the change occurs gradually and continuously over time.