Graduate Seminar
Mean curvature flow for triple junctions of surfaces
Dr. Alex Freire
18 Jun 2007, 16:00 – 18:00
For a class of networks of surfaces in three-dimensional space, consider the geometric motion described informally as follows: the cells are parametrized by a disk or an annulus, and their interiors move by mean curvature flow. Each boundary component parametrizes either a `liquid edge' or a `free boundary'. Along each `liquid edge', three surfaces meet making constant 120 degree angles, while on the `free boundaries', the surfaces intersect a fixed support surface orthogonally. I'll discuss a proof of short-time existence of classical solutions. This is analogous to a well-known geometric evolution for curves, but the existence proof for that case does not translate directly to surfaces.
http://geometricanalysis.mi.fu-berlin.de/os/os-ss07.htm
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