Event

Siran Li (CRM, McGill)

Friday, March 15, 2019 13:30to14:30
Burnside Hall Room 1104, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

Title: Some Problems On Harmonic Maps from B^3 to S^2.


Abstract: Harmonic map equations are an elliptic PDE system arising from the minimisation of Dirichlet energies between two manifolds. In this talk we present some recent works concerning the symmetry and stability of harmonic maps. We construct a new family of ''twisting'' examples of harmonic maps and discuss the existence, uniqueness and regularity issues. In particular, we characterise the singularities of minimising general axially symmetric harmonic maps, and construct non-minimising general axially symmetric harmonic maps with arbitrary 0- or 1-dimensional singular sets on the symmetry axis. Moreover, we prove the stability of harmonic maps from $\mathbb{B}^3$ to $\mathbb{S}^2$ under $W^{1,p}$-perturbations of boundary data for $p>=2$. (Joint work with Prof. Robert Hardt.)

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