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PDE Seminar Series
November 6, 2018 @ 10:30 am - 11:30 am
The coming PDE seminar will be next Tuesday. Details are below. Please let me know if you would like to join the lunch with the speaker after the talk.
Alexander Majchrowski (University of Sydney)
Level-Set and Surgery Approaches to Brendle-Huisken G-Flow
In the 2-Convex setting, Huisken-Sinestrari developed a surgical technique for mean curvature flow and were able to obtain classification results. However, surgery depends on a non-canonical choice of surgery parameters, in contrast to the unique weak solution to the level-set setting for mean curvature flow derived by Spruck-Evans and Chen-Giga-Goto. Independently Lauer and Head were able to show that as we take our surgery parameters to be arbitrarily large that these two solutions agree.
The surgery results for mean curvature flow do not extend to the Riemannian setting. In order to tackle this Brendle-Huisken inspired by Andrews work on harmonic mean curvature flow introduced G-flow. We derive viscosity solutions for the G-flow and apply Lauer’s argument for a reconciliation between the G-flow with surgeries and the viscosity solution.