The 1977’ Acta paper by Lawson-Osserman studied the Dirichlet problem
for minimal surfaces of high codimensions. Several astonishing results essentially distinct
from the case of codimension 1 were obtained there. In particular, they found
Lipschitz but non-C1 solutions to the problems associated to Hopf maps between unit
spheres. Recently, with collaborators, we developed Lawson-Osserman’s constructions
and discovered certain interesting new phenomena on the existence, non-uniqueness
and non-minimizing property of solutions to related Dirichlet problems. This talk is
based on joint works with Xiaowei XU and Ling YANG.