| Abstract: |
| In this talk we discuss some recent progress on the analysis of the mean curvature flow with free boundary supported on a double cone. This includes results on convergence and finite-time singularities. Singularities can be classified by their type, as in the case of the compact flow. Here, we have a new kind of singularity, that we call type 0. We give examples of support hypersurfaces that yield the development of singularities of a specified type for certain initial data. This includes examples of the elusive Type 2 singularities. |
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