Abstract
In recent years major progress was made on the global behaviour of geometric evolution equations, in particular the harmonic map heatflow, the Ricci flow and the mean curvature flow. Longtime existence and regularity could be shown in a number of important cases. On the other hand, it became clear that in general singularities do occur in finite time, and an understanding of their structure should be crucial both for further development in the theory of these equations and for possible applications. In this article we will point out some of the strong analogies in the equations mentioned above and show in the case of the mean curvature flow how rescaling techniques can be used to understand the asymptotic behaviour of many singularities. We emphasize techniques applicable in all the equations under consideration and mention some open problems.
Information
