## General Axially Symmetric Harmonic Maps

- Oct. 12, 2018
- 2:15 p.m.
- LeConte 312

## Abstract

Harmonic map equations are an elliptic PDE system arising as the Euler-Lagrange equation for the minimisation problem of Dirichlet energies between two manifolds. In this talk, we consider the harmonic maps from 3-dimensional unit ball to the 2-sphere with a generalised type of axial symmetry. Examples include certain ''twisting'' maps. We discuss the existence, uniqueness and regularity issues of this family of harmonic maps. In particular, we characterise of 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. Potential problems on numerical studies of harmonic maps shall also be discussed. (Joint work with Prof. Robert M. Hardt.)