Mean curvature flow and its singularity

Abstract:  We will start this talk, which will be told mainly via pictures, with a short introduction to the mean curvature flow and the type of problems one would like to resolve with it. We will see that a major obstacle when trying to apply the flow is its singularity formation. We then discuss two results. First, we show that under some curvature assumptions the singularity formation is sufficiently simple to find ways to flow through the singularities without losing any topological information. (Here, we present joint work with Robert Haslhofer and Or Hershkovits and with Sylvain Mailot.) Second, we show that without such simplifying curvature assumptions the singularities can be arbitrarily complicated by constructing singularity models of any given genus. (This is joint work with Huy Nguyen and Mario Schulz.)

Past Events

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