Due to the seminal work of Lawson and Osserman, the Dirichlet problem for minimal surface of high codimension turns out to be dramatically different from the situation of codimension one. Namely, non-existence, non-uniqueness and irregularity of solutions to the problem may occur for certain boundary data. This talk aims to explain some recent developments in these three aspects.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/3050