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

  • Date: 10/06/2015
  • Time: 15:30
Jun-Cheng Wei, UBC

University of British Columbia


On Type II Singularity Formulation of Harmonic Map Flows


I will consider the following classical  harmonic map flow from a general two-dimensional domain D to S^2: u_t=\Delta u +|\nabla u|^2 u, u: D \to S^2We develop a parabolic gluing method to construct finite time blow-up solutions of Type II in general domains. We show  that type II blow-up solutions with blow-up  rate(T-t)/\log^2 (T-t)is stable and generic in arbitrary domains (without any symmetry).  I will also discuss the construction of  multiple blow-ups, reverse bubbling, bubbling trees, bubbling at infinity. As a by-product we can perform new geometric surgeries. (Joint work with Manuel del Pino and Juan Davila.)

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Location: ESB 2012