Some Problems On Harmonic Maps from $\mathbb{B}^3$ to $\mathbb{S}^2$

notice the special date. March 19th, 9-10am. Room Thackeray 427

Tuesday, March 19, 2019 - 09:00

427 Thackeray

Speaker Information
Siran Li
Rice U

Abstract or Additional Information

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 

 (Joint work with Prof. Robert Hardt.)

Research Area