Diff. Geom, Math. Phys., PDE Seminar: Jun-Cheng Wei

  • Date: 10/29/2013
  • Time: 15:30
Jun-Cheng Wei, UBC

University of British Columbia


On Fractional Minimal Surfaces


We consider fractional minimal surfaces introduced by Caffarelli, Roquejoffre and Savin (2009). Up to now the only examples of fractional minimal surfaces are hyperplanes. In this talk, we first prove the existence of the analog of fractional Lawson's minimal cones and establish their stability/instability in low dimensions. In particular we find that there are stable fractional minimal cones in dimension 7, in contrast with the case of classical minimal surfaces. Then we prove the existence of fractional catenoids and fractional Costa-Hoffman-Meeks surfaces. Interestingly the interaction of planes in fractional minimal surfaces is governed by an nonlinear elliptic equation with negative power which arises in the study of MEMS. (Joint work with J. Davila and M. del Pino.)

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Location: ESB 2012