Mathematical Sciences: Weak Solutions of Geometric Evolution Equations

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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.